In the graph below, each unit on the horizontal axis is 2.0 m 3 and each unit on

Question

In the graph below, each unit on the horizontal axis is 2.0 m3 and each unit on the vertical axis is 5.0 atm.

(a) A gas is compressed along the path AC. What is the work done on the gas in this case?
How is the work done related to the area under the curve? What is the difference between work done by the gas and on the gas? ]

_______________ j

(b) If the gas is instead compressed along the path ABC, what is the work done on the gas?
_________________ j
What is the work done along the path where the volume is constant? J

(c) What is the work done on the gas if the path of compression is along ADC?
________________J
What is the work done along the path where the volume is constant? J

Explanation / Answer

##part a)

Work done is equal to the area under the graph

here graph is triangle + rectangle

dV = 4*2 = 8 m^3

dP = 7*5 = 35 atm = 35*1.013e5 Pa

W = 0.5*dV*dP + dV*2*5 = 0.5*8*35*1.013e5 + 8*2*5*1.013e5 = 2.2286e+7 J

work done by the gas is positive

and on the gas is negative

part b)

W = 9*5*1.013e5*8 = 3.6468e+7 J

dv = 0

W = P*dv = 0

##part c)

work = area = dV*2*5*1.013e5 = 8*2*10*1.013e5 = 1.6208e+7 J

if dV = 0

work = p*dV = 0

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