Question

A system undergoes a thermodynamic transformation from state \( S_1 \) to \( S_2 \) via two different paths 1 and 2. The heat absorbed and work done along path 1 are 50 J and 30 J, respectively. If the heat absorbed along path 2 is 30 J, the work done along path 2 is:

• A. Zero
• B. 10 J
• C. 20 J
• D. 30 J

Hint:

Internal energy change is path independent; always use the first law to relate heat and work for any thermodynamic process.

Answer 1

The Correct Option is B

Step 1: Apply the first law of thermodynamics.
\[ \Delta U = Q - W. \] Step 2: For path 1,
\[ \Delta U = 50 - 30 = 20\, \text{J}. \] Since internal energy change depends only on initial and final states, \( \Delta U \) remains the same for both paths.
Step 3: For path 2,
\[ 20 = 30 - W_2 \Rightarrow W_2 = 10\, \text{J}. \] Step 4: Final Answer.
The work done along path 2 is 10 J.