(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A cylinder with a frictionless piston is placed horizontally in an atmosphere pressure 1 * 10^{5}N/m^{2}. A gas in the cylinder is initially at a temperature of 300K with a volume of 6.0 * 10^{-3}m^{3}. Then the gas is heated slowly to 400K. How much work is done by the gas in the process?

2. Relevant equations

Ideal Gas equations:

p*V/T = constant

p*V = NKT = nRT

Ek (average) = (3/2) * kT

Ek (total) = (3/2) * NkT = (3/2)pV

3. The attempt at a solution

At first I calculated the initial energy as:

E_{1}= (3/2)pV = (3/2)*(1 * 10^{5}) * (6.0 * 10^{-3}) = 900J

Then, assuming the pressure is constant, I said:

pV_{1}/T_{1}= pV_{2}/T_{2}

V_{2}= V_{1}*T_{2}/ T_{1}

V_{2}= 6.0 * 10^{-3}* 400 / 300 = 8*10^{-3}

Thus, the second energy:

E_{2}= (3/2)*10^{5}*8*10^{-3}= 1200J

And the work:

W = E_{2}- E_{1}= 1200 - 900 = 300J.

Now, in the answer to the question, it says the work is not 300J, but 200J.

Can someone enlighten me about my mistake?

Thanks.

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# Homework Help: Ideal Gas Exercise

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