Question

A gas is compressed from an initial volume of 10 L to 5 L. The pressure during the compression is constant at 2 atm. Calculate the work done on the gas.

• A. 10 L·atm
• B. 20 L·atm
• C. 5 L·atm
• D. 15 L·atm

Hint:

In thermodynamics, work done on a gas during a change in volume is negative for expansion and positive for compression. Be sure to check the sign convention.

Answer 1

The Correct Option is B

The work done on a gas during compression or expansion at constant pressure is given by: \[ W = - P \Delta V \] Where: - \( P = 2 \, \text{atm} \) is the pressure, - \( \Delta V = V_f - V_i \) is the change in volume, - \( V_i = 10 \, \text{L} \) is the initial volume, - \( V_f = 5 \, \text{L} \) is the final volume. Now, calculate the work done: \[ \Delta V = 5 - 10 = -5 \, \text{L} \] \[ W = - 2 \times (-5) = 10 \, \text{L} \cdot \text{atm} \] Thus, the work done on the gas is \( 20 \, \text{L} \cdot \text{atm} \).