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Question
A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 liters to a volume of 10 liters. In doing so it absorbs 400J of thermal energy from its surroundings. Determine the change in the internal energy of the system.
Solution
Given:
P = 1 atm = 1.013 x 105 Pa,
V1 = 5 liters = 5 x 10-3 m3,
V2 = 10 liters = 10 x 10-3 m3,
Q = 400 J
The work done by the system on its surroundings,
W = P(V2 - V1)
= (1.013 x 105) (10 x 10-3 - 5 x 10-3)
= 1.013 (5 x 102)
= 5.065 x 102 J
The change in the internal energy of the system,
ΔU = Q - W = 400 - 506.5 = -106.5 J
The negative sign shows that there is a decrease in the internal energy of the system.
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