A gas expands from A to B as shown in the graph. Calculate the work (in joules) done by the gas. (1 atm= 1.01 × 10⁵ N/m².) A) 12 B) 24 C) 1.21 × 10⁶ D) 2.42 × 10⁶ E) 3.64 × 10⁶

Question

Quizplus · Accepted Answer

The work done by the gas is equal to the area under the curve on a pressure-volume graph. Therefore, we need to find the area of the trapezoid formed by points A and B. 
Area = 1/2 x (6-2) x (1+2) + 2 x (1+2)
Area = 10 J
However, we need to convert the units of pressure from atm to N/m^2:
1 atm = 1.01 x 10^5 N/m^2
Therefore, the work done by the gas is:
W = P x ΔV = (1.01 x 10^5 N/m^2) x (0.04 m^3) = 2.42 x 10^4 J or 2.42 x 10^16 ergs. 
The closest choice is D, 2.42 × 10^16 J.

A Gas Expands from a to B as Shown in the Graph