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In changing the state of a gas adiabatic...

In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to `22.3J` 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 later case? (Take `1 cal.= 4.9J`)

Text Solution

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The work done (W) on the system while the gas changes from state A to B is 22.3 J.
This is an adiabatic process. Hence, change in heat is zero.
`thereforeDeltaQ=0`
`DeltaW = –22.3 J` (Since the work is done on the system)
From the first law of thermodynamics, we have:
`DeltaQ = DeltaU + DeltaW`
Where,
`DeltaU = "Change in the internal energy of the gas"`
`thereforeDeltaU=DeltaQ-DeltaW=-(-22.3J)`
`DeltaU=+22.3J`
When the gas goes from state A to state B via a process, the net heat absorbed by the system is:
`DeltaQ = "9.35 cal = 9.35 × 4.19 = 39.1765 J"`
`"Heat absorbed", DeltaQ = DeltaU + DeltaQ `
`thereforeDeltaW=DeltaQ-DeltaU`
`= 39.1765 – 22.3`
`= 16.8765 J`
Therefore, 16.88 J of work is done by the system.
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