Question

In diagrams ( $1$ to $4$ ), variation of volume with changing pressure is shown. A gas is taken along the path $ABCD$ . The change in internal energy of the gas will be

• A. Positive in all the cases $\left(\right.1\left.\right)$ to $\left(\right.4\left.\right)$ .
• B. Positive in cases $\left(\right.1\left.\right),\left(\right.2\left.\right),\left(\right.3\left.\right)$ but zero in case $\left(\right.4\left.\right)$ .
• C. Negative in cases $\left(\right.1\left.\right),\left(\right.2\left.\right),\left(\right.3\left.\right)$ but zero in case $\left(\right.4\left.\right)$ .
• D. Zero in all the cases.

Answer 1

Answer: (D)

Internal energy is a state function. That is, the change in internal energy in a process depends solely on the initial state and final state of the process. Also, the change in internal energy is path independent.
In a cyclic process, the initial state and final state of the process are the same. Hence, in a cyclic process, the change in internal energy is zero.
In all the given diagrams, the $V-P$ graphs represents the cyclic process. Therefore, the change in internal energy in all the four processes is zero.