An expansion process on an ideal diatomic ideal gas has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is 300 kPa, the volume is $0.0700 \mathrm {~m} ^ { 3 }$ and the temperature is $390 \mathrm {~K}$ The final pressure is $130 \mathrm { kPa }$ and the final temperature is $310 \mathrm {~K}$ How much work is done by the gas during this process? (R = 8.31 J/mol ∙ K)
A) 13,000 J
B) 6300 J
C) 9400 J
D) 16,000 J
E) 19,000 J

Question

Quizplus · Accepted Answer

The work done by the gas during this process is given by the area under the line on the pV diagram. The line is linear, so the area is a trapezoid. The area of a trapezoid is given by:$$A = \frac{1}{2}(b_1 + b_2)h$$where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height. In this case, the parallel sides are the initial and final pressures, and the height is the change in volume. So, the area is:$$A = \frac{1}{2}(300 \mathrm { kPa } + 130 \mathrm { kPa })(0.0700 \mathrm {~m} ^ { 3 } - 0.100 \mathrm {~m} ^ { 3 }) = 13,000 \mathrm { J }$$Therefore, the work done by the gas is 13,000 J.

An Expansion Process on an Ideal Diatomic Ideal Gas Has 0.0700 m30.0700 \mathrm {~m} ^ { 3 }0.0700 m3

An Expansion Process on an Ideal Diatomic Ideal Gas Has $0.0700 \mathrm {~m} ^ { 3 }$