In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal,how much is the net work done by the system in the latter case ? (Take 1 cal = 4.19 J)

Explanation

The work done (W) on the system while the gas changes from state A to state B is W = -22.3 J
In adiabatic change `DeltaQ = 0`
From the first law of thermodynamics,
`DeltaQ=DeltaU+W`
`therefore 0=DeltaU-22.3`
`therefore DeltaU`=22.3 J ...(1)
Means the internal energy of the system increases.
Now when the gas goes from state A to state B, the neat heat absorbed by the system is 9.35 cal.
`DeltaQ`=+9.35 cal
=9.35 x 4.19 J
=39.18 J ....(2)
and from the first law of thermodynamics ,
`DeltaQ=DeltaU+W`
`therefore W=DeltaQ-DeltaU`
=39.18-22.3 [`because` From equ. (1) and (2)]
=16.9 J