Question

Calculate the work done when an ideal gas expands from \(1\times 10^{-3}\) to \(1\times 10^{-2}\ \text{m}^{3}\) at 300 K against constant pressure of \(1\times 10^{5}\ \text{Nm}^{-2}\).

• A. 900kJ
• B. \(-900\)kJ
• C. 270kJ
• D. \(-900\)J

Hint:

Use w = -P(V2 - V1) with pressure in N per square metre and volume in cubic metres, which gives joules.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For expansion against constant external pressure, \(w=-P_{ext}\,\Delta V\).

Step 2: Calculation
\(\Delta V=1\times 10^{-2}-1\times 10^{-3}=9\times 10^{-3}\ \text{m}^{3}\).
\(w=-(1\times 10^{5})(9\times 10^{-3})=-900\) J.

Step 3: Conclusion
The negative sign shows that the gas does work on its surroundings. The temperature is not needed.

Final Answer:
The work done is \(-900\) J. \[ \boxed{\text{(D) }-900\ \text{J}} \]