I\'m having a bit of trouble with this. It should not be hard, but I am missing

Question

I'm having a bit of trouble with this.  It should not be hard, but I am missing something.  The problem states:

A cylinder provided with a movable piston contains an ideal gas at a pressure P1, specific volume v1, and temperature T1. The pressure and volume are simultaneously increased so that at every instant P and v are related by the equation, P = Av, where A is a constant.

A). Express A in terms of the pressure P1, the temperature T1, and the gas constant R.

C). Find the temperature when the specific volume has doubled, if T1=200K

I believe I have an answer to (A), but (C) is throwing me for loops!

Explanation / Answer

1.

From ideal gas equation

PV=RT

Now, given P=AV;

hence,

P^2/A=RT

At inital condition;

P=P1,T=T1

or

A=P1^2/RT1

2.

Again from P=AV;

it follows;

P2=AV2=2AV1=2P1

Now from ideal gas equation;

P1V1/T1=P2V2/T2

or

P1V1/T1=(2*P1)(2*V1)/T2

or

T2=4T1=800K

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