A cylinder with a movable frictionless piston contains an ideal gas that is init

Question

A cylinder with a movable frictionless piston contains an ideal gas that is initially in state 1 at 1x10 to the fifth Pa, 373K, and 0.25m cube. The gas is taken through a reversible thermodynamic cycle.

a) Calculate the temperature of the gas when it is in the following states 2 (1.0x10 to the fifth) and state 3 (1.5x10 to the fifth)
b) Calculate the net work done on the gas during the cycle?
c)Was heat added to or removed, or neither added or removed from the gas during the cycle?

Please show steps to answer but keep it simple:) Thank you

Explanation / Answer

Given a cylinder with a movable frictionless piston containsan ideal gas that is initially in state at pressure P1 = 1.0 x105pa,T1= 99oC and V1=0.25m3.The gas is taken through a reversiblethermodynamic cycle which is shown on the PV-diagram. Let the pressure ,volume and temperature of the gas in thestate 2 be P2,V2and T2. From the gas equation ,we have P1V1/T1 =P2V2/T2 or T2 =(P2V2/P1V1) xT1 = (1 x 105 x 0.50)/(1 x 105 x0.25) x 99 or T2 = 2 x 99oC =198oC. Similarly, the temperature of the gas T3 can becalculated as P1V1/T1 =P3V3/T3 or T3 =(P3V3/P1V1) xT1 = (1.5 x 105 x 0.25)/(1.0 x 105x 0.25) x 99 or T3= 1.5 x 99 = 148.5oC. The net work(in J) done by the gas during the cycle is equalto the area of triangle 123. = (1/2) x b x h = (1/2) x (0.50 - 0.25) x (1.5 x105 - 1.0 x 105) = (1/2) x (0.25) x (0.5 x105) = 0.0625 x 105J = 6250J.

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