Question

An ideal gas expands isothermally and reversibly from 10m\(^3\) to 20m\(^3\) at 300K, performing 5×10\(^3\) J of work on surroundings, calculate number of moles of gas used?

• A. 1
• B. 3
• C. 2
• D. 1.5

Hint:

For isothermal processes, remember the work formula involving the logarithm of volume ratio, and ensure the temperature remains constant throughout.

Answer 1

The Correct Option is B

Step 1: Using the work equation for an isothermal process.
For an ideal gas expanding isothermally, the work done is given by: \[ W = nRT \ln \left(\frac{V_f}{V_i}\right) \] Where: - \(W = 5 \times 10^3 \, \text{J}\) (work done) - \(R = 8.314 \, \text{J/mol·K}\) (gas constant) - \(T = 300 \, \text{K}\) (temperature) - \(V_i = 10 \, \text{m}^3\) (initial volume) - \(V_f = 20 \, \text{m}^3\) (final volume)
Step 2: Rearranging the equation.
\[ n = \frac{W}{RT \ln \left(\frac{V_f}{V_i}\right)} \] Substitute the known values: \[ n = \frac{5 \times 10^3}{8.314 \times 300 \times \ln \left(\frac{20}{10}\right)} = 3 \, \text{mol} \]
Step 3: Conclusion.
The correct answer is (B) 3 moles.