Question

A closed cylindrical vessel contains N moles o n
ideal diatomic gas at a temperature T. On supplying
heat,, temperature remains same, but n moles se
dissociated into atoms. The heat supplied is
(1) 5/2(N − n)RT (2)5/2 nRT
(3) 1/2nRT (4)3/2nRT​

Answer 1

Answer:

Since the gas is enclosed in a vessel, therefore, during heating process, volume of the gas remains constant. Hence, no work is done by the gas. It mean heat supplied to the gas is used to increase its internal energy only.

Initial internal energy of the gas is U1=N(5/2R)T

Since n moles get dissocited into atoms, therefore, after heating vessel contains (N−n) moles of a mono-atomic gas. Hence the internal energy for the gas, after heating will be equal to

U2=(N−n)(5/2R)T+2n(3/2R)T

=5/2NRT+1/2nRT

Hence, the heat supplied = increase in internal energy ltbr .(U2−U1)=1/2nRT