What is the work done by the gas from a to c?

Question

Figure 18-53 displays a closed
cycle for a gas. From c to b, 40 J is
transferred from the gas as heat.
From b to a, 130 J is transferred from
the gas as heat, and the magnitude of
the work done by the gas is 80 J.
From a to c, 400 J is transferred to
the gas as heat. What is the work
done by the gas from a to c? (Hint:
You need to supply the plus and minus signs for the given data.)

engxcommish · Answer

We can think about this problem visually, as work done is area under the curve. 
 
C=>B
From C to B, no work is done, as there is no area under the curve.
This means that the 40J transfered from the gas is a 40J energy loss, so from C to B we have
 
&Delta;U= Q + W
&Delta;U= - 40 J
Q = - 40 J
W =  0
 
B=>A
Next, from B to A. Q = -130J, and W = +80J (The tricky thing here is the way the question is worded. Remember that W = -PdV. In this path, the Volume is decreasing so -P(smallV - largeV) is a positive number).
 
The energy change, &Delta;U, here is -50J
 
A=>C
Now, when we go from A to C, we are completing the cycle.
 
&Delta;U = 3/2*nR&Delta;T
 
Our state is back to where we were originally, so The total &Delta;U = 0
 
So &Delta;Uac + &Delta;Ucb + &Delta;Uba = 0
and &Delta;Uac = 90J
 
&Delta;U= Q + W = 90J = +400 + W.
 
Wac = -310J.
 
Now, the question asks how much work is done BY the gas. When Work is a negative number, it is being done BY the system. So,
 
310J of Work are done by the gas from a to c.
 
This was my first answer, I hope it is helpful.

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What is the work done by the gas from a to c?

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