Mayer's Formula

Mayer's Formula

Edited By Vishal kumar | Updated on Jul 02, 2025 06:14 PM IST

Mayer's formula explains the relationship between the specific heat of gas at constant pressure and constant volume, which is one of the most essential equations in thermodynamics. According to it, gas constant (R) is the difference between specific heat at constant pressure (Cp) and specific heat at constant volume (Cv). Thus, this makes it possible to understand better how energy flows take place in gases and how their heat capacity changes depending on the circumstances.

Mayer's Formula

In this article, we will cover the concept of the 'Mayer's Formula’. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), seventeen questions have been asked on this concept. And for NEET two questions were asked from this concept.

Let's read this entire article to gain an in-depth understanding of Mayer's Formula.

Molar Specific heat of the gas at constant volume $= C_{v}$
and Molar-specific heat capacity at constant pressure $C_{p}$
Mayer's formula gives the relation between $C_{p}$ and $C_{v}$ as $C_{p} = C_{v} + R$

or we can say that molar Mayer’s formula shows that specific heat at constant pressure is greater than that at constant volume.

Specific Heat in Terms of Degree of Freedom

1. Molar Specific heat of the gas at constant volume ($C_v$)

For a gas at temperature T, the internal energy

$U = \frac{f}{2} n R T \Rightarrow Change in energy Δ U = \frac{f}{2} n R Δ T \dots$

Also, as we know any gas heat supplied at a constant volume

$(Δ Q)_{V} = n C_{V} Δ T = Δ U \dots \dots (ii)$

From the equation (i) and (ii)

$C_{v} = \frac{f R}{2}$

where

f = degree of freedom

R= Universal gas constant

Molar Specific heat of the gas at constant pressure ($C_p$)

From Mayer's formula, we know that $C_{p} = C_{v} + R$
$\Rightarrow C_{P} = C_{V} + R = \frac{f}{2} R + R = (\frac{f}{2} + 1) R$

Atomicity or adiabatic coefficient ($\gamma$)

It is the ratio of $C_{p}$ to $C_{v}$
$γ = \frac{C_{p}}{C_{v}} = 1 + \frac{2}{f}$

$Value of γ is always more than 1$

$for Monoatomic gas γ = \frac{5}{3}$

for Diatomic gas $γ = \frac{7}{5}$

for Triatomic gas $γ = \frac{4}{3}$

What is a Gaseous Mixture?

If two non-reactive gases $A$ and $B$ are enclosed in a vessel of volume $V$ .
In the mixture $n_{1}$ mole of Gas $A$ (having Specific capacities as $C_{p 1}$ and $C_{v 1}$ , Degree of freedom $f_{1}$ and Molar mass as $M_{1}$ ) is mixed with
$n_{2}$ mole of Gas B (having Specific capacities as $C_{p 2}$ and $C_{v 2}$ ,Degree of freedom $f_{2}$ and Molar mass as $M_{2)}$

Then Specific heat of the mixture at constant volume will be

$C_{v_{mix}} = \frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}}$

Similarly, the Specific heat of the mixture at constant pressure will be

$C_{p_{mix}} = \frac{n_{1} C_{p_{1}} + n_{2} C_{p_{2}}}{n_{1} + n_{2}}$

And adiabatic coefficient ($\gamma$) of the mixture is given by

$γ_{mixure} = \frac{C_{p_{mix}}}{C_{v_{m \in}}} = \frac{\frac{(n_{1} C_{p_{1}} + n_{2} C_{p_{2}})}{n_{1} + n_{2}}}{\frac{(n_{1} C_{v_{1}} + n_{2} C_{v_{2}})}{n_{1} + n_{2}}} = \frac{(n_{1} C_{p_{1}} + n_{2} C_{p_{2}})}{(n_{1} C_{v_{1}} + n_{2} C_{v_{2}})}$

Also

$\frac{1}{γ_{mix} - 1} = \frac{\frac{n_{1}}{γ_{1} - 1} + \frac{n_{2}}{γ_{2} - 1}}{n_{1} + n_{2}}$

Similarly, the Degree of freedom of mixture is given as
$f_{mix} = \frac{n_{1} f_{1} + n_{2} f_{2}}{n_{1} + n_{2}}$

Similarly, the molar mass of the mixture
$M_{m i x} = \frac{n_{1} M_{1} + n_{2} M_{2}}{n_{1} + n_{2}}$

Learn Mayer's Formula With a Video Lecture

Solved Examples Based on Mayer's Formula

Example 1: The specific heats $C_{p} and C_{v}$ of a gas of diatomic molecules A are given ( in units of $J\:mol^{-1}$ ) by 29 and 22 respectively. Another gas of diatomic molecule B has the corresponding values of 30 and 21 respectively. If they are treated as ideal gases then :

1) A is rigid but B has a vibrational mode.

2) A has a vibrational mode but B has none.

3) A has one vibrational mode and B has two.

4) Both A and B have a vibrational mode each.

Solution:

Specific heat capacity at constant pressure -

$\begin{aligned} C_{p} = C_{v} + R \\ = (\frac{f}{2} + 1) R \end{aligned}$
wherein
$f =$ degree of freedom
$R =$ Universal gas constant
$\frac{C_{p}}{C_{v}} = 1 + \frac{2}{f}$

For gas A,
$\begin{aligned} \frac{29}{22} = 1 + \frac{2}{f} \Rightarrow \frac{2}{f} = \frac{7}{22} \\ \Rightarrow f = \frac{44}{7} ≃ 6 \end{aligned}$

3 translations, 2 rotations, Remaining vibrational mode

For gas B,

$\begin{aligned} \frac{C_{p}}{C_{v}} = \frac{30}{21} = 1 + \frac{2}{f} \Rightarrow \frac{2}{f} = \frac{9}{21} \\ \Rightarrow f = \frac{42}{9} ≃ 5 \end{aligned}$

3 translations, 2 rotations, no vibrational mode

Hence, the answer is the option (2).

Example 2: Two moles of helium are mixed with n moles of hydrogen.

If $\frac{C_{p}}{C_{v}} = 3 / 2$ for the mixture, then the value of n is :

1) 1

2) 3

3) 2

4) 1.5

Solution:

As we have learned

Atomicity or adiabatic coefficient (gamma) -

$\begin{aligned} γ = \frac{C_{p}}{C_{v}} \\ = 1 + \frac{2}{f} \end{aligned}$
wherein
for Monoatomic gas
$γ = \frac{5}{3}$
for Diatomic gas
$γ = \frac{7}{5}$
for Triatomic gas
$γ = \frac{4}{3}$
$\begin{aligned} c_{p}^{mix} = \frac{n_{1} c p_{1} + n_{2} c p_{2}}{n_{1} + n_{2}} = \frac{2 * 5 R / 2 + n (7 R / 2)}{2 + n} = \frac{10 + 7 n}{2 + n} R \\ c_{v}^{mix} = \frac{n_{1} c v_{1} + n_{2} c v_{2}}{n_{1} + n_{2}} = \frac{2 * 3 R / 2 + n (5 R / 2)}{2 + n} = \frac{6 + 5 n}{2 + n} R \end{aligned}$

$r^{mix} = \frac{3}{2} = \frac{c_{p}^{mix}}{c_{v}^{mix}} = \frac{10 + 7 n}{6 + 5 n} \Rightarrow 18 + 15 n = 20 + 14 n$

or n=2

Hence, the answer is option (3).

Example 3: Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C_p/C_v value will be :

1) 40/27

2) 23/15

3) 19/13

4) 67/45

Solution:

For monoatomic gas (He)

$c_{v} = \frac{3 R}{2}, c_{p} = \frac{5 R}{2}$

For diatomic gas $(O_{2})$
$\begin{aligned} c_{v} = \frac{5 R}{2}, c_{p} = \frac{7 R}{2} \\ γ_{mixure} = \frac{C_{p_{mix}}}{C_{v_{m x}}} = \frac{(n_{1} C_{p_{1}} + n_{2} C_{p_{2}})}{(n_{1} C_{v_{1}} + n_{2} C_{v_{2}})} \\ = \frac{n \frac{5}{2} R + 2 n \frac{7}{2} R}{n \frac{3}{2} R + 2 n \frac{5}{2} R} = \frac{19}{13} \end{aligned}$

Hence, the answer is the option (3).

Example 4: Two moles of an ideal gas with $\frac{C_{p}}{C_{v}} = \frac{5}{3}$ are mixed 3 moles of another ideal gas with $\frac{C_{p}}{C_{v}} = \frac{4}{3}$ . The value of $\frac{C_{p}}{C_{v}}$ for the mixture is:-

1) 1.50
2) 1.45
3) 1.47
4) 1.42

Solution:

For ideal gas:- $C_{p} - C_{v} = R$
For first case:-
$\begin{aligned} \frac{C_{p 1}}{C_{v 1}} = \frac{5}{3} and C_{p 1} - C_{v 1} = R \\ C_{p 1} = \frac{5}{3} C_{v 1} and \frac{5}{3} C_{v 1} - C_{v 1} = R \Rightarrow \frac{2}{3} C_{v 1} = R \Rightarrow C_{v 1} = \frac{3}{2} R \end{aligned}$

So, $C_{p 1} = \frac{5}{2} R$
For second case:-
$\begin{aligned} \frac{C_{p 2}}{C_{v 2}} = \frac{4}{3} and C_{p 2} - C_{v 2} = R \\ C_{p 2} = \frac{4}{3} C_{v 2} and \frac{4}{3} C_{v 2} - C_{v 2} = R \Rightarrow C_{v 2} = 3 R and C_{p 2} = 4 R \\ Y_{m i x} = \frac{n_{1} C_{p 1} + n_{2} C_{p 2}}{n_{1} C_{v 1} + n_{2} C_{v 2}} = \frac{2 \times \frac{5}{2} R + 3 \times 4 R}{2 \times \frac{3}{2} R + 3 \times 3 R} = 1.417 = 1.42 \end{aligned}$

Hence, the answer is the option (4).

Example 5: Two moles of helium gas are mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat (in J/mol K) of the mixture at constant volume? (R=8.3 J/mol K)

1) 15.7

2) 17.4

3) 19.7

4) 21.6

Solution:

$\begin{aligned} C_{v mix} = \frac{n_{1} C_{v_{1}} + n_{2} C_{v_{2}}}{n_{1} + n_{2}} \\ = \frac{2 \times \frac{3}{2} R + 3 \times \frac{5}{2} R}{2 + 3} \\ = \frac{3 R + 15 \frac{R}{2}}{5} \\ = (\frac{21}{10}) R = \frac{21}{10} \times 8.314 \\ = 17.4 J / molK \end{aligned}$

Hence the answer is the option (2).

Summary

Mayer’s Law is a basic equation in thermodynamics relating the specific heat capacities of a gas at constant pressure denoted by Cp and at a constant volume Cv. His law states that the difference between the specific heat capacity at constant pressure Cp and the specific heat capacity at constant volume is equal to the gas constant R. With this principle, we can be able to know how gases take in heat and release it under varying circumstances.

Frequently Asked Questions (FAQs)

1. Can Mayer's Formula be used to calculate the work done in a gas expansion process?

Yes, Mayer's Formula can be used indirectly to calculate work done in gas expansion. The difference (Cp - Cv) represents the work done per mole per degree temperature change when a gas expands at constant pressure. Multiplying this by the temperature change and number of moles gives the total expansion work.

2. Can Mayer's Formula be used to explain why the temperature of a gas decreases during adiabatic expansion?

Yes, Mayer's Formula helps explain this phenomenon. During adiabatic expansion, no heat is added to the system (Q = 0). The gas does work against its surroundings (W > 0), and according to the First Law of Thermodynamics (ΔU = Q - W), the internal energy must decrease. Mayer's Formula relates this change in internal energy to the temperature change through Cv.

3. How does Mayer's Formula account for the degrees of freedom in a gas molecule?

Mayer's Formula indirectly accounts for the degrees of freedom through the ratio of specific heat capacities (γ = Cp/Cv). The more degrees of freedom a molecule has, the smaller this ratio becomes. For monatomic gases, γ = 5/3, for diatomic gases, γ = 7/5, and for polyatomic gases, γ is even closer to 1.

4. Why is the specific heat capacity at constant pressure (Cp) always greater than the specific heat capacity at constant volume (Cv)?

Cp is always greater than Cv because heating at constant pressure allows the gas to expand, requiring additional energy for this expansion work. At constant volume, all the heat goes into increasing the internal energy of the gas, while at constant pressure, some energy goes into expansion work.

5. How does Mayer's Formula change for different types of gases (monatomic, diatomic, polyatomic)?

Mayer's Formula itself (Cp - Cv = R) doesn't change for different types of gases. However, the values of Cp and Cv do change based on the molecular structure, affecting their ratio (γ). This ratio decreases as molecular complexity increases: monatomic (5/3) > diatomic (7/5) > polyatomic (closer to 1).

6. What is Mayer's Formula and why is it important in the kinetic theory of gases?

Mayer's Formula is an equation that relates the difference between the specific heat capacities of a gas at constant pressure (Cp) and constant volume (Cv) to the universal gas constant (R). It's important because it helps us understand the relationship between heat capacity and molecular structure of gases, which is crucial in thermodynamics and the kinetic theory of gases.

7. How does Mayer's Formula relate to the internal energy of a gas?

Mayer's Formula (Cp - Cv = R) indirectly relates to internal energy. The specific heat at constant volume (Cv) represents the change in internal energy per unit temperature change. The difference (Cp - Cv) represents the additional energy needed for expansion work when heating at constant pressure.

8. Can Mayer's Formula be applied to all types of gases?

Mayer's Formula is most accurate for ideal gases. It can be applied to real gases with reasonable accuracy at low pressures and high temperatures when they behave more like ideal gases. However, for dense gases or those near their critical point, the formula may need corrections.

9. How does Mayer's Formula help in calculating the speed of sound in a gas?

Mayer's Formula is crucial in deriving the speed of sound equation for gases. The ratio of specific heat capacities (γ) that appears in Mayer's Formula is a key component in the equation for the speed of sound: v = √(γRT/M), where R is the gas constant, T is temperature, and M is molar mass.

10. Can Mayer's Formula be used to determine the molecular structure of an unknown gas?

Yes, Mayer's Formula can be used indirectly to determine molecular structure. By measuring Cp and Cv experimentally and calculating their ratio (γ), we can infer the number of degrees of freedom and thus the molecular structure of the gas. For example, γ ≈ 5/3 suggests a monatomic gas, while γ ≈ 7/5 suggests a diatomic gas.

11. How does temperature affect the applicability of Mayer's Formula?

Mayer's Formula is most accurate at high temperatures when gases behave more ideally. At very low temperatures or near condensation, intermolecular forces become significant, and the formula may need corrections. However, for most practical purposes, it remains valid over a wide temperature range for many gases.

12. What's the significance of the ratio of specific heat capacities (γ = Cp/Cv) in Mayer's Formula?

The ratio γ = Cp/Cv, also known as the heat capacity ratio or adiabatic index, is crucial in many thermodynamic calculations. It appears in equations for adiabatic processes, speed of sound, and efficiency of heat engines. Mayer's Formula helps us understand why this ratio is always greater than 1 for gases.

13. What's the connection between Mayer's Formula and the First Law of Thermodynamics?

Mayer's Formula is derived from the First Law of Thermodynamics. It represents the difference in work done by a gas when heated at constant pressure versus constant volume, which is equal to the external work done by the gas (PΔV) in expanding against constant pressure.

14. What role does the universal gas constant (R) play in Mayer's Formula?

In Mayer's Formula (Cp - Cv = R), the universal gas constant R represents the work done by one mole of an ideal gas when it expands against a constant pressure while its temperature increases by 1 Kelvin. It quantifies the difference between heat capacities due to expansion work.

15. What assumptions are made in deriving Mayer's Formula?

The main assumptions in deriving Mayer's Formula are:

16. What's the relationship between Mayer's Formula and the ideal gas law?

Mayer's Formula is derived using the ideal gas law (PV = nRT). The formula quantifies the difference in energy required to heat a gas at constant pressure versus constant volume, which is directly related to the PV work term in the ideal gas law. Both are fundamental to our understanding of ideal gas behavior.

17. How does Mayer's Formula relate to the concept of reversibility in thermodynamic processes?

Mayer's Formula assumes reversible processes in its derivation. It represents the ideal case where the gas expands infinitely slowly against a pressure that's always infinitesimally less than the gas pressure. This concept of reversibility is crucial in understanding the maximum possible efficiency of heat engines and other thermodynamic devices.

18. How does Mayer's Formula help in understanding the concept of enthalpy of an ideal gas?

Mayer's Formula helps explain why the enthalpy of an ideal gas depends only on temperature. Since H = U + PV, and for an ideal gas PV = nRT, we can show using Mayer's Formula that the change in enthalpy (dH = CpdT) is independent of pressure for an ideal gas.

19. How does Mayer's Formula help in understanding the behavior of gases during isothermal processes?

While Mayer's Formula isn't directly used in isothermal processes (where temperature is constant), it helps us understand why work is done by a gas during isothermal expansion without a change in internal energy. The PV work done is balanced by heat absorbed, maintaining constant internal energy, which is consistent with Mayer's Formula and the First Law of Thermodynamics.

20. Can Mayer's Formula be used to explain why Cp is always positive for an ideal gas?

Yes, Mayer's Formula helps explain this. Since Cv is always positive (it takes energy to increase the temperature of a gas), and Mayer's Formula states that Cp = Cv + R, where R is the positive universal gas constant, Cp must always be positive and greater than Cv for an ideal gas.

21. How does Mayer's Formula help in understanding the behavior of gases in a piston-cylinder device?

Mayer's Formula is crucial in analyzing piston-cylinder devices. It helps explain why the work done by a gas expanding at constant pressure (W = PΔV) is equal to R times the temperature change. This insight is valuable in understanding heat engine cycles and other thermodynamic processes in such devices.

22. Can Mayer's Formula be used to explain why the internal energy of an ideal gas depends only on temperature?

Yes, Mayer's Formula supports this concept. Since Cv represents the change in internal energy per unit temperature change for an ideal gas, and Mayer's Formula shows that Cv is constant (Cv = Cp - R), it follows that the internal energy of an ideal gas depends only on temperature, not on pressure or volume.

23. How does Mayer's Formula help in understanding the behavior of gases during free expansion?

In a free expansion, an ideal gas expands into a vacuum with no change in internal energy or temperature. Mayer's Formula helps explain why no work is done and no heat is transferred in this process, as the expansion occurs without overcoming any external pressure.

24. How does Mayer's Formula relate to the equipartition theorem?

Mayer's Formula is consistent with the equipartition theorem, which states that each degree of freedom of a molecule contributes R/2 to its molar heat capacity. The difference Cp - Cv = R in Mayer's Formula represents the additional degree of freedom associated with the expansion work done at constant pressure.

25. Can Mayer's Formula be applied to liquids or solids?

Mayer's Formula is specifically derived for gases and is not directly applicable to liquids or solids. In condensed phases, the difference between Cp and Cv is usually much smaller due to the limited expansion of these phases, and different relationships are used to describe their thermal properties.

26. How does Mayer's Formula help in understanding the efficiency of heat engines?

Mayer's Formula is crucial in understanding heat engine efficiency because it relates to the ratio of specific heat capacities (γ), which appears in the equation for the efficiency of ideal heat engines. A higher γ leads to higher theoretical efficiency, explaining why monatomic gases are theoretically more efficient working fluids than diatomic or polyatomic gases.

27. How does Mayer's Formula relate to the concept of enthalpy?

Mayer's Formula is closely related to enthalpy. The specific heat at constant pressure (Cp) represents the change in enthalpy per unit temperature change, while Cv represents the change in internal energy. The difference (Cp - Cv = R) accounts for the PV work done during expansion, which is included in enthalpy but not in internal energy.

28. How does Mayer's Formula help in understanding adiabatic processes?

Mayer's Formula is crucial in deriving the equations for adiabatic processes. The ratio γ = Cp/Cv, which can be expressed using Mayer's Formula, appears in the equations for adiabatic expansion and compression (PV^γ = constant). This helps us understand how temperature and pressure change during adiabatic processes.

29. What's the historical significance of Mayer's Formula in the development of thermodynamics?

Mayer's Formula, developed by Julius Robert von Mayer in the 1840s, was a crucial step in the development of thermodynamics. It helped establish the concept of heat as a form of energy and contributed to the formulation of the First Law of Thermodynamics. It also provided evidence for the kinetic theory of gases.

30. How does Mayer's Formula relate to the concept of internal degrees of freedom in molecules?

Mayer's Formula indirectly relates to internal degrees of freedom. The values of Cp and Cv, and consequently their difference R, depend on the number of internal degrees of freedom a molecule possesses. More complex molecules with more degrees of freedom have larger heat capacities, affecting how Cp and Cv relate to R in the formula.

31. Can Mayer's Formula be used to predict the behavior of gases at extremely high pressures?

Mayer's Formula becomes less accurate at extremely high pressures where gases deviate significantly from ideal behavior. In these conditions, intermolecular forces and the volume of the gas molecules themselves become significant, and more complex equations of state (like the van der Waals equation) are needed for accurate predictions.

32. How does Mayer's Formula help in understanding the concept of heat capacity?

Mayer's Formula (Cp - Cv = R) provides insight into the nature of heat capacity by showing that it depends on the conditions under which heat is added to a system. It explains why gases have two distinct heat capacities (Cp and Cv) and quantifies their difference, helping us understand how energy is distributed in gas molecules.

33. How does Mayer's Formula help in calculating the efficiency of a Carnot engine?

While Mayer's Formula isn't directly used in calculating Carnot efficiency, it's indirectly involved. The ratio γ = Cp/Cv, which can be expressed using Mayer's Formula, appears in the equation for the efficiency of ideal heat engines. This helps explain why monatomic gases (with higher γ) would theoretically make more efficient working fluids in a Carnot engine.

34. Can Mayer's Formula be applied to mixtures of gases?

Yes, Mayer's Formula can be applied to mixtures of ideal gases. For a mixture, you would use the weighted average of the specific heat capacities based on the mole fractions of the component gases. The universal gas constant R remains the same for any ideal gas or mixture of ideal gases.

35. What's the significance of Mayer's Formula in studying atmospheric processes?

Mayer's Formula is important in atmospheric science because it relates to the adiabatic processes that occur in the atmosphere. The ratio γ = Cp/Cv, which can be derived from Mayer's Formula, is used in calculating the adiabatic lapse rate, which describes how the temperature of a parcel of air changes as it rises or falls in the atmosphere.

36. How does Mayer's Formula relate to the concept of entropy?

While Mayer's Formula doesn't directly involve entropy, it's related to entropy changes in ideal gases. The ratio Cp/Cv, which can be expressed using Mayer's Formula, appears in equations for entropy changes during isentropic (adiabatic and reversible) processes in ideal gases.

37. What's the connection between Mayer's Formula and the specific heat capacity of gases at different temperatures?

Mayer's Formula assumes constant heat capacities, which is a good approximation for many gases over a wide temperature range. However, at very high temperatures, when vibrational modes of molecules become excited, the heat capacities can change. In such cases, more complex models that account for temperature-dependent heat capacities are needed.

38. How does Mayer's Formula relate to the concept of internal energy in ideal gases?

Mayer's Formula indirectly relates to internal energy through Cv. For an ideal gas, the change in internal energy is given by ΔU = nCvΔT. Mayer's Formula shows that Cv is always less than Cp by R, helping us understand how internal energy changes differ from enthalpy changes in ideal gases.

39. What's the significance of Mayer's Formula in studying polytropic processes?

Mayer's Formula is relevant to polytropic processes, which are described by PV^n = constant, where n is the polytropic index. The values of n for various processes (isothermal, isobaric, isochoric, adiabatic) can be related to the ratio γ = Cp/Cv, which is connected to Mayer's Formula.

40. How does Mayer's Formula relate to the concept of work in thermodynamic processes?

Mayer's Formula is closely related to work in thermodynamics. The difference Cp - Cv = R represents the PV work done per mole per degree temperature change when a gas expands at constant pressure. This helps us understand how work is related to heat capacity and temperature changes in various thermodynamic processes.

41. What's the connection between Mayer's Formula and the speed of sound in different gases?

Mayer's Formula is crucial in understanding why the speed of sound differs in various gases. The speed of sound in a gas is given by v = √(γRT/M), where γ = Cp/Cv. Mayer's Formula helps us understand why γ differs for different gases, explaining why sound travels faster in lighter, monatomic gases than in heavier, polyatomic ones.