An expansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram.The initial pressure is the initial volume is and the initial temperature is The final pressure is and the final temperature is The change in the internal (thermal)energy of the gas is closest to

Question

An expansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram.The initial pressure is  the initial volume is  and the initial temperature is  The final pressure is  and the final temperature is  The change in the internal (thermal)energy of the gas is closest to

Quizplus · Accepted Answer

Since the process is a linear expansion, the work done by the gas is given by:
W = area under the straight line on the pV diagram
W = (P1 + P2) / 2 * (V2 - V1)

Using the ideal gas law, we can find the initial and final number of moles of the gas:
n1 = P1V1 / R*T1
n2 = P2V2 / R*T2

Since it is an ideal gas, the internal energy depends only on temperature:
ΔU = U2 - U1 = (n2 * Cv * ΔT) - (n1 * Cv * ΔT)
ΔU = ΔT * Cv * (n2 - n1)
ΔU = ΔT * Cv * [(P2V2 - P1V1) / (R * ΔT)]

Substituting the values given:
ΔU = (9.9 kPa + 11 kPa) / 2 * (7.8 L - 5.2 L) * (8.31 J/mol K) * [(9.9 kPa * 11 L - 11 kPa * 5.2 L) / (8.31 J/mol K * 40 K)]
ΔU ≈ -3100 J

Therefore, the answer is (A) -3100 J.

An Expansion Process on an Ideal Diatomic Gas Has a Linear