Answered Essay: Consider a container with a frictionless piston that contains a given amount of an ideal gas.

Consider a container with a frictionless piston that contains a given amount of an ideal gas. Assume the initial volume of the gas is 7 L, the initial temperature of the gas is 22.1 °C, and the system is in equilibrium with an external pressure of 1.1 bar. In step 1, the gas is cooled reversibly to a final temperature -29.9 °C. The external pressure remains constant at all times. In step 2 the gas is heated at constant volume to a final temperature 4.1 °C.

A) What is the final pressure of the gas?

B) What is the final volume?

C) Calculate w for the overall process (steps 1 + 2)

Expert Answer

Answer

A)

In step 2 the gas is heated at constant volume to a final temperature 4.1 °C.

V2 = V3 = 5.767 L

So,T3 = 4.1 °C =277.1K

T2 =-29.9 °C. = 243.1K

Pressure   P2= 1.1 bar.

Final pressure of the gas P3 = ?

P2V2/T2 = P3V3/T3

P3 = P2V2T3/ V3T2

P2 = (1.1 x 5.767 x 277.1)/(5.767 x 243.1) = 1.25 bar

Final pressure of the gas is 1.25 bar

B)

Initial volume of the gas V1 = 7 L

The initial temperature of the gasT1 = 22.1 °C = 295.1K

The final temperature T2 -29.9 °C =243.1K

Now calculate the final volume V2 by using equation

P1V1/T1 = P2V2/T2

V2 = P1V1T2 /P2T1

(1.1bar x7L x 243.1K)/(1.1bar x 295.1K) = 5.767 L

Final volume = 5.767L

C) Calculate w for the overall process (steps 1 + 2)

W for the steps 1 =

W1 = P ( V2 – V1)

= 1.1 (5.767- 7.0 ) = – 1.356 KJ

W2 for the steps 2 = 0

Because the volume is constant in step 2, soW2 = 0

w for the overall process (steps 1 + 2) = – 1.36 KJ+ 0 = – 1.36 KJ

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