The figure below is a pressure versus volume graph where the different curves re

Question

The figure below is a pressure versus volume graph where the different curves represent different processes done on a gas. Starting at the origin to point 1, the pressure and volume are increased to 2.500 x 10^3 Pa and 4.25 m^3 respectively. From 1 to 2 the gas expands at constant pressure to a volume of 7.25 m^3. From 2 to 3 the pressure rises to 4.410*10^3 Pa. And finally from 3 to 4 the gas expands again to 10.68 m^3. Using the ranking module, rank the curves from the most positive to the most negative amount of work done on the gas. What is the total work done on the gas?

Explanation / Answer

note: work =W, pressure =P, volume = V; Pa.m3=J(joules) and k=103

W = -P x (change in volume) or simply the area under the line.

listing the coordinates (V,P) of all the process points,

1 = (4.25 , 2.5k);

2 = (7.25 , 2.5k);

3 = (7.25 , 4.41k);

4 = (10.68 , 4.41k);

calculating work

for process 0 - 1 the area under the curve is -0.5 x 4.25 x 2.5k = -5312.5 J =W0-1

(use area of triangle = 0.5 x base x height)

for process 1 - 2 the area under the line is -2.5k x (7.25 - 4.25) = -7500 J = W1-2

for process 2 -3 there is no change in volume, thus W2-3= 0 J

for process 3 -4 the work is -4.41k x (10.68 - 7.25) = -15126.3 J = W3-4

the order from most -ve to +ve work is W3-4 , W1-2, W0-1, W2-3 ;

the total work is sum of all the Ws = -27938.8 J

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