Question

N moles of an ideal diatomic gas are in a closed cylinder at temperature T. Suppose, on supplying heat to the gas, its temperature remains constant, but n moles get dissociated into atoms. Then, heat supplied to the gas is -

a) Zero
b) ½nRT
c) 3/2 nRT
d) 3/2 (N-n) RT​

Answer 1

Please refer to the attachment.

Answer 2

The temperature of the gas remains constant the internal energy also remains constant.

So,

The heat supplied is used to do work on the gas.

The diatomic gas initially had N moles and after dissociation of n moles it has (N-n) moles.

So the internal energy of the gas is initially :-

U = (3/2)NRT

Finally,

U' = (3/2)(N-n)RT

The work done on the gas is given :-

W = (U - U') = (3/2)nRT

Thus,

The heat supplied to the gas is equal to the work done on it and therefore the correct answer is (b) ½nRT.