Question

Calculate the amount of work done during isothermal expansion of a gas from a volume of 4 dm\(^3\) to 6 dm\(^3\) against a constant external pressure of 3 atmosphere.

• A. -30.4 J
• B. -60.8 J
• C. -607.8 J
• D. -6.0 J

Hint:

In isothermal processes, the work done is calculated by multiplying the external pressure by the change in volume. Remember to use the correct units and conversion factors.

Answer 1

The Correct Option is C

Step 1: Understanding the work done in an isothermal process.
The work done (\(W\)) during an isothermal expansion is given by the equation: \[ W = -P_{\text{ext}} \Delta V \] Where: - \(P_{\text{ext}} = 3 \, \text{atm}\) (external pressure) - \(\Delta V = V_2 - V_1 = 6 \, \text{dm}^3 - 4 \, \text{dm}^3 = 2 \, \text{dm}^3\) - To convert atm·dm\(^3\) to joules, we use the conversion factor: \[ 1 \, \text{atm} \cdot \text{dm}^3 = 101.325 \, \text{J} \] Step 2: Calculating the work.
\[ W = - (3 \, \text{atm}) \times (2 \, \text{dm}^3) \times (101.325 \, \text{J/atm·dm}^3) = -607.8 \, \text{J} \] Step 3: Conclusion.
The correct answer is (C) -607.8 J.