The ideal gas law is a good approximation in most cases, but some applications m
ID: 1369278 • Letter: T
Question
The ideal gas law is a good approximation in most cases, but some applications may call for a more precise model of the relationship between the pressure, volume, and temperature of a gas. For a certain amount of a particular non-ideal gas, over a certain temperature range, this relationship is given by the equation PV = (5.59 10^3 J/K2)T^2 + (20.5 J/K)T.
The temperature of this sample of gas is decreased from 58.0°C to 48.0°C. Determine the work done at constant pressure on the gas during this temperature change.
_______J
Explanation / Answer
T1 = initial temperature = 58 C = 58 + 273 = 331 K
T2 = final temperature = 48 C = 48 + 273 = 321 K
PV1 = ( 5.59 103 )T12 + (20.5) T1 = ( 5.59 103 ) (331)2 + (20.5) (331) = 116346.5 J
PV2 = ( 5.59 103 )T22 + (20.5) T2 = ( 5.59 103 ) (321)2 + (20.5) (321) = 109621.5
Work done = PV2 - PV1 = 109621.5 - 116346.5 = - 6725 J
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