1. May 16, 2007

imy786

1. The problem statement, all variables and given/known data

A sample of 5 moles of nitrogen gas (γ = 1.40) occupies a volume of 3.00 × 10^−2 m3 at a pressure of 2.00 × 10^5 Pa and temperature of 280 K.
The sample is adiabatically compressed to half its original volume. Nitrogen behaves as an ideal gas under these conditions.

a)What is the change in entropy of the gas?

b)Show from the adiabatic condition and the equation of state that TV γ −1 remains constant, and hence determine the final temperature of the gas.

2. Relevant equations

3. The attempt at a solution

(a)

W=PV
Change in V= (3-1.5) *10^2= 1.5^10*-2

W= 2.00 × 10^5 * 1.5^10*-2
= 3*10^3 J

U=Q+W
Q= -W
Q= - 3*10^3

S= Q/T
= - 3*10^3/ 280= 10.7 JK^-1

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(b)

equation of state : PV= nRT

(nRT)^gamma=A

A* V γ−1 = P

P= nRT/v

nRT/v= A* V γ−1

nRT/vA = V γ−1

TV γ −1 remains constant..

2. May 16, 2007

Andrew Mason

Assume it is compressed reversibly and adiabatically (the external pressure is slightly higher than internal pressure during compression). Is there any flow of heat into/out of the gas or into or out of the surroundings? So what is the change in entropy?

I find it a little difficult to follow your reasoning. Substitute P = nRT/V into $PV^\gamma = A$ to get

$$nRTV^{\gamma-1} = A$$

AM

3. May 17, 2007

imy786

(a) there is flow of heat to the system of temp 300K.
The change in entropy has doubled as the volume has halved.

4. May 17, 2007

bidhati

What is the adiabatic accessibility index doing? rising falling remaining constant? this will tell you what the change in entropy is.

5. May 17, 2007