1.

Gaseous hydrogen contained initially under standard conditions in sealed vessel of volume `V = 5 L` was cooled by `Delta T = 55 K`. Find how much the internal energy of the gas will change and what amount of heat will be lost by the gas.

Answer» By the first law of thermodynamics
`Delta Q = Delta U + Delta W`
Here `Delta W = =` as the volume remains constant.
`:. Delta Q = Delta U`
Now `Delta U = (m)/(M) (R ) C_(V) (- Delta T)`
`= - (m)/(M) (R )/(gamma - 1) Delta T` `(as C_(V) = (R )/(gamma - 1))`
We have `P_(0)V = (m)/(M) RT_(0)`
`= - (1.013 xx 10^(5) xx (5 xx 10^(-3)) xx 55)/(273 (1.4 - 1)) = - 255 J`


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