Gas in a container is at a pressure of 1.4 atm and a volume of 8.0 m 3 . (a) Wha
ID: 1747991 • Letter: G
Question
Gas in a container is at a pressure of 1.4 atm and a volume of 8.0 m3. (a) What is the work done on the gasif it expands at constant pressure to twice its initial volume?1 J
(b) What is the work done on the gas if it is compressedat constant pressure to one-quarter its initial volume?
2 J (a) What is the work done on the gasif it expands at constant pressure to twice its initial volume?
1 J
(b) What is the work done on the gas if it is compressedat constant pressure to one-quarter its initial volume?
2 J
Explanation / Answer
Initial pressure, P = 1.4 atm = 1.4 X 1.013 X 10 5 Pa = 1.4182 X 10 5 Pa Initial Volume, V1 = 6 m^3 Work done, W = ? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (a) Pressure = constant Final volume, V2 = 2 V1 Work done at constant pressure, W = PV = P ( V2 - V1 ) = P ( 2 V1 - V1 ) = P V1 = 1.4182 X 10 5 * 6 = 8.51 X 10 5 J ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (b) Pressure = constant Final volume, V2 = V1 / 4 Work done at constant pressure, W = PV = P ( V2 - V1 ) = P [ ( V1 / 4) - V1 ) ] = P [ ( - 3 / 4 ) V1] = ( - 3 / 4 ) P V1 = - 0.75 * 1.4182 X 10 5 * 6 = - 6.38 X 10 5 J
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