Question

One mole of a mono-atomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram, then

• A. for process A to B, heat is lost and internal energy increases.
• B. for process B to C, heat is lost and internal energy increases.
• C. for process C to D, heat is gained and internal energy increases.
• D. for process D to A, heat is gained and internal energy increases.

Hint:

Use PV = nRT to find how temperature changes for each process and then apply the first law.

Answer 1

The Correct Option is C

Step 1: Temperatures
$T_A\propto9pV$, $T_B\propto3pV$, $T_C\propto pV$, $T_D\propto9pV$.

Step 2: Check each option
A to B and B to C lose temperature, so their internal energy decreases and the statements are wrong. D to A has no change in internal energy.

Step 3: C to D
Temperature rises from $pV$ to $9pV$ at constant pressure, so energy increases and heat must be supplied.

Final Answer:
The statement about C to D is correct. \[ \boxed{\text{(C) }\text{for process C to D, heat is gained and internal energy increases}} \]