Question

Under isothermal condition, a gas at 300 K expands from 0.1 L. to 0.25 L against a constant external pressure of 2 bar. The work done by the gas is: [Given that 1 L bar=100J]

• A. -30 J
• B. 5 kJ
• C. 25 J
• D. 30 J

Answer 1

The Correct Option is D

To find the work done by a gas during an isothermal expansion against a constant external pressure, follow these steps:

1. Identify the given values:
   • Initial Volume, \(V_1 = 0.1\,\text{L}\)
   • Final Volume, \(V_2 = 0.25\,\text{L}\)
   • External Pressure, \(P_{\text{ext}} = 2\,\text{bar}\)
   • Conversion: \(1\,\text{L·bar} = 100\,\text{J}\)
2. Change in volume: \(\Delta V = V_2 - V_1 = 0.25 - 0.1 = 0.15\,\text{L}\)
3. Work done: \(W = -P_{\text{ext}} \Delta V = -2 \times 0.15 = -0.30\,\text{L·bar}\)
4. Convert to joules: \(W = -0.30 \times 100 = -30\,\text{J}\)
5. Negative sign indicates work done by the system; magnitude is \(30\,\text{J}\).
6. Final Answer: \(30\,\text{J}\)