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Demonstate that the inerval energy U of ...

Demonstate that the inerval energy `U` of the air in a room is independent of temperature provided the outside pressure `p` is constant. Calculate `U`, if `p` is equal the normal atmosphere pressure and the room's volume is equal to `V = 40 m^3`.

Text Solution

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Intermal energy of air, treating as an ideal as
`U = (m)/(M) C_V T = (m)/(M)(R)/(gamma - 1)T = (pV)/(gamma - 1)`….(1)
Using `C_V = (R)/(gamma - 1)`, since `C_p - C_V = R` an d `(C_p)/(C_V) = gamma`
Thus at constant pressure `U` = constant, because the volume of the room is a constant.
Putting the value of `p = p_(atm)` and `V` in Eq.(1), we get `U = 10 MJ`.
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