Question

An ideal gas expands from 1 × 10\(^-3\) m\(^3\) to 1 × 10\(^-2\) m\(^3\) at 300 K against a constant external pressure of 1 × 10\(^5\) N/m\(^2\). Work done is

• A. -9 × 10\(^2\) J
• B. -9 × 10\(^3\) J
• C. -0.7 × 10\(^3\) J
• D. -1 × 10\(^3\) J

Hint:

For an expansion or compression process against constant external pressure, use the formula \(W = -P \Delta V\) to calculate the work done.

Answer 1

The Correct Option is A

Step 1: Applying the work formula for expansion.
The work done by the gas during expansion is given by: \[ W = -P \Delta V \] where \(P\) is the external pressure, and \(\Delta V\) is the change in volume. In this case: \[ P = 1 \times 10^5 \, \text{N/m}^2, \quad \Delta V = (1 \times 10^{-2} - 1 \times 10^{-3}) = 9 \times 10^{-3} \, \text{m}^3 \]
Step 2: Calculation.
\[ W = - (1 \times 10^5) \times (9 \times 10^{-3}) = -9 \times 10^2 \, \text{J} \]
Step 3: Conclusion.
The work done is (A) -9 × 10\(^2\) J.