Question

Two identical vessels A & B contain equal amount of ideal monoatomic gas. The piston of A is fixed but that of gas B is free. Same amount of heat is absorbed by A & B . If B's internal energy increases by 100 J the change in internal energy of A is:

• A. $100J$
• B. $\frac{500}{3}J$
• C. $250J$
• D. None of these

Answer 1

The correct option is B $\frac{500}{3}J$

We have the change in internal energy in B as $\Delta U=n{C}_v\Delta T=100J$

$C_v$ for a monoatomic gas is $\frac{f}{2}R=\frac{3}{2}R$ (f is the degree of freedom)
Thus we get

$100=n\frac{3}{2}R\Delta T$
or

$\Delta T=\frac{200}{3nR}$

Now $\Delta Q$ for B is given as $n{C}_p\Delta T$

and $C_p$ is given as $(1+\frac{f}{2})R=(1+\frac{3}{2})R=\frac{5}{2}R$

Thus we get

$\Delta Q=n\frac{5}{2}R\frac{200}{3nR}=\frac{500}{3}R$

Now as the heat absorbed in both A and B is same and as the piston is fixed in A the work done is zero in A.

Thus we get $\Delta Q=\Delta U$(using first law)

Thus $\Delta U=\frac{500}{3}R$