Question

Calculate the work done if 1 mole of gas compressed isothermally and reversibly at 300 K from initial pressure 1 bar to final pressure 2 bar [$R=8.314~J~K^{-1}mol^{-1}$]

• A. 1.729 kJ
• B. 0.865 kJ
• C. 2.593 kJ
• D. 3.458 kJ

Hint:

Compression work is positive; expansion work is negative.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The work done in an isothermal reversible process involves calculating work using pressures.

Step 2: Key Formula or Approach:
\[ W = -2.303 nRT \log_{10} \left( \frac{P_1}{P_2} \right) \]

Step 3: Detailed Explanation:
Given: \( n = 1 \text{ mol} \), \( T = 300 \text{ K} \), \( P_1 = x \), \( P_2 = 2x \).
\[ W = -2.303 \times 1 \times 8.314 \times 300 \times \log_{10} \left( \frac{x}{2x} \right) \]
\[ W = -2.303 \times 8.314 \times 300 \times \log_{10}(0.5) \]
Note: \( \log(0.5) = -0.3010 \).
\[ W = -2.303 \times 8.314 \times 300 \times (-0.3010) \]
\[ W = +1728.6 \text{ J} \approx 1.729 \text{ kJ} \]
(Work is positive because the gas is compressed).

Step 4: Final Answer:
The work done is 1.729 kJ.