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 is given by the area under the curve on a pV diagram. Since the path is linear, the area is a trapezoid with bases $p_i$ and $p_f$ and height $V_f - V_i$. Therefore, the work done is:$$W = \frac{1}{2}(p_i + p_f)(V_f - V_i)$$$$W = \frac{1}{2}(300 \mathrm {~kPa} + 130 \mathrm {~kPa})(0.0700 \mathrm {~m} ^ { 3 } - 0.0200 \mathrm {~m} ^ { 3 })$$$$W = 13,000 \mathrm {~J}$$

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 $0.0700 \mathrm {~m} ^ { 3 }$