Can pls anyone explain why in isothermal process dt is not 0?
Suppose we consider an Ideal gas. (Ah, one more definition, Ideal gas is a gas in which we neglect attraction between particles, therefore, no potential energy, thus here internal energy just refers to total kinetic energy) and make it undergo Isothermal process, then BY DEFINITION, temperature or Average kinetic energy of the molecules remains a constant. If Average kinetic energy is a constant, then the total kinetic energy must also remain a constant. So look at the internal energy of this gas. Since internal energy for an ideal gas is just it’s total kinetic energy, by definition, the internal energy must be a constant. Does that make sense now?
However, if we break that assumption, that particles are not attracted to each other, then potential energy comes into the picture. Now, in an isothermal process, even though temperature (average kinetic energy) is a constant, it’s potential energy can definitely change, thus now it’s internal energy can definitely change.
A practical example would be during phase change. Suppose you consider water boiling. Since water is a liquid, you can definitely NOT neglect the attraction between particles and hence potential energy cannot be neglected at all. Hence during boiling, all the heat energy supplied (or taken up by the liquid) increases the potential energy of the system (makes particles farther and farther away), but keeps the total kinetic energy a constant.
So the temperature definitely remains a constant, thus by definition this is an isothermal process, but since potential energy is increasing (like crazy) the internal energy of the system is definitely increasing.
in Newton's law of cooling
-dq/dt =k(t2 - t1)
in isothermal process t2 - t1 is 0
therefore dq (heat) must be 0
oops I made a mistake in question
i want to know why dq is not zero
in isothermal process?
Reply
Isothermal processes first of all means processes where temperature remains constant and goes unchanged isn't it? At the same time, internal energy also remains constant. The q ie heat depends on the work done on the system or by the system and doesn't depend upon the temperature. Therefore in isothermal processes, heat can surely change and thus it doesn't remain constant and since it doesn't remain constant, change in heat ie dq cannot be 0. Take for example the case of fusion of ice. When ice at 0°C converts to water at 0°C its temperature remains unchanged but still you have to provide heat in order for the conversion to take place. The heat provided doesn't increase the temperature of ice rather it helps break the bonds which converts solid ice to liquid water.
Thank you.
