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## Homework Statement

At the start of a compression, a cylinder contains 0.04 m^2 of some ideal gas at a pressure of 100kPa and a temperature of 110 degrees. Compression takes place according to the law:

P(V)^1.27 = constant

The gas undergoes a two stage process: compression from 0.04 m^3 to 0.01 m^3, followed by constant volume heating to raise the pressure to 4000 kPa.

a. Calculate the pressure and temperature of the gas after the first process.

b. Calculate the temperature of the gas after the second process.

c. Calculate the work done.

d. Draw the P-V diagram, clearly indicating the two stages.

## Homework Equations

P(V)^1.27 = constant

## The Attempt at a Solution

I solved question (a) by using the equation P1(V1)^1.27 = P2(V2)^1.27 and found that after the first process the pressure is 582 kPa, V= 0.01 m^3 and T= 556 K.

For question (b), do I only need to use the equation T2/T1 = (P2/P1)^(0.27/1) to get the temperature after the second process? It says constant volume heating then does it mean volume is unchanging?

For question (c), is it work done in the first process or the second or both combined?

W= (P2V2-P1V1) / 1-1.27 is the equation I am going to use.

For question (d), I'm not sure what to do, please help.

Thank you.