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Question

With what minimum pressure (in kPa), a given volume of an ideal gas (Cp,m=72 R), originally at 400 K and 100 kPa pressure can be compressed irreversibly and adiabatically in order to raise its temperature to 600 K:

A
362.5 kPa
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B
275 kPa
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C
437.5 kPa
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D
550 kPa
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Solution

The correct option is D. 275 kPa.

Given,

Cp,m=72 R

Therefore, Cv=CpR=72 RR=52 R.
From the first law of thermodynamics,
ΔU=W+Q
For an adiabatic irreversible compression, Q = 0.
ΔU=W

The change in internal energy is given by, ΔU=nCv,m(T2T1)

and the work done is given by, W=PextΔV
nCv,m(T2T1)=Pext(V2V1)
nCv,m(T2T1)=P2[nRT2P2nRT1P1]
52R(T2T1)=P2×R[T2P2T1P1]
P2=275 kPa.


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