Question:
During an adiabatic compression, the pressure of a gas is found to be proportional to the cube of its temperature.The ratio of Cp/Cv for the gas is.
a)5/3
b)3/2
c)4/3
d)2
Will you please explain how the answer came?
Answer:
We know that ( T2 / T1 ) = (V1 / V2)ϒ-1 where ϒ = Cp - Cv
Given Pressure of gas is proportional to T3
Hence, V is inversely proportional to T3
Therefore (V1 / V2) = ( T2 / T1 )3
( T2 / T1 ) = (V1 / V2)1/3
Comparing this with the standard equation, ( T2 / T1 ) = (V1 / V2)ϒ-1
ϒ – 1 = 1/3
ϒ = 4/3
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