The work done by a gas molecule in an isolated system is given by, W e x = KT 2 2 , where x is the displacement, k is the Boltzmann constant and T is the temperature, and are constants. Then, the dimensions of will be a. [M2 L T 2 ] b. [M0 L T 0 ] c. [M L T 2 ] d. [M L2 T
Answer (1)
12th Feb, 2024
Hello,
To determine the dimensions of W in the given equation. We know that W represents work done, which has dimensions of energy. The equation W = KT^2/2 involves the displacement x, Boltzmann constant k, and temperature T.
The dimensions of displacement x are [L], the dimensions of the Boltzmann constant k are [M L^2 T^-2 K^-1], and the dimensions of temperature T are [T].
By substituting the dimensions into the equation, we get [L] = [M L^2 T^-2 K^-1] * [T]^2 / 2. Simplifying this, we find that the dimensions of W are [M L^2 T^-2].
So, the correct option is d. [M L^2 T^-2].
Hope this helps,
Thank you
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