Question

Two identical vessels $A$ and $B$ contain equal amount of ideal monoatomic gas. The piston of $A$ is fixed but that of $B$ is free. Same amount of heat is absorbed by $A$ and $B$. If $B^{\prime }s$ internal energy increases by $100J$ 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 A $100J$

From $1st$ Law of thermodynamics, we have $dQ=dU+dW=dU+PdV\to \left(1\right)$

For case $A:dV=0$ So, $dW=0$ and hence

$\Rightarrow d{Q}_A=d{U}_A\to \left(2\right)$

For case $B:$ It is free expansion so, $△W$ has to be zero and that's why

$\Rightarrow d{Q}_B=d{U}_B=100J\to \left(3\right)$

But $d{Q}_A=d{Q}_B=100J$ So, using $\left(2\right)$ we get,

$\Rightarrow d{U}_A=100J,$ Change in internal energy of $A.$

Hence, the answer is $100J.$