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Question

1 mole of NH3 gas at 27°C is expanded in reversible adiabatic condition to make volume 8 times (y=1.33). Final temperature and work done respectively are:

A
150 K, 909 cal
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B
150 K, 400 cal
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C
250 K, 1000 cal
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D
200 K, 800 cal
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Solution

The correct option is C 150 K, 909 cal
As we know that, for an adiabatic expansion,

TVγ1=constant
T2T1=(V1V2)γ1

Given:-
T1=27=(27+273)K=300K
T2=T=?
V1=V
V2=8V
γ=1.33=43
T300=(V8V)431
T=3002=150K

Now, using first law of thermodynamics, ΔE=q+w
As we know that, for adiabatic expansion, q=0

ΔE=w

If gas expands, the internal energy decreases.

w=ΔE=nCVdT

w=[1×Rγ1×(150300)]

w=[150×21.331]

w=909cal

Hence the value of final temperature and work done are 150K and 909cal respectively.

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