Heat and Thermo
Classical Mechanics
Level
4
In an adiabatic expansion of air the volume increases by 5%. Then the percentage change in pressure is __%.
Note: If the pressure decreased, then the percentage change will be negative.
The answer is -6.6.
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1 solution
Assuming the air is at low pressure, the following polytropic process equation holds:
P 1 V k 1 = P 2 V k 2
Where subscript "1" is the state before and "2" after the change took place. "P" is pressure, "V" is volume and "k" is ratio of specific heats. For air at low pressure (approx. ideal gas):
k = 5 7
The volume of the air has increased by 5%, so:
V 2 = 1 . 0 5 V 1
After plugging this into the first equation above and simplifying:
P 1 = 1 . 0 5 k P 2
So:
P 1 P 2 − P 1 = 1 . 0 5 k 1 − 1 . 0 5 k
or -0.066 x 100% = − 6 . 6 %