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Mechanical Properties Of Fluids

Question
CBSEENPH11019536

Find the internal energy of air in a room of size 3m x 4m x 6m at pressure 75cm of mercury.

Solution
The internal energy of V volume of gas at pressure P is given by, 
            space space space space space space
space space space space space space space space space space space space space U equals fraction numerator P V over denominator y minus 1 end fraction             ... (1)
we have,
Volume of the room, V=3m x 4m x 6m = 72m

Pressure, P=75cm of mercury
                =75 x 13.6 x 980 dyne/cm2 
                = 9.996 x 10N/m
Air is mixture of diatomic gases.
Therefore,
                 y = 1.4
Putting values in equation (1), we have
So, internal energy is given by, 

space straight U space equals fraction numerator 9.996 cross times 10 to the power of 4 cross times 72 over denominator 1.4 minus 1 end fraction space space space

space space space space space equals space 1.8 cross times 10 to the power of 7 straight J