A gas expands from `3 dm^(3)` to `5dm^(3)` against a constant pressure of `3atm`. The work done during the expansion if used to heat `10mol` of water at temperature `290K`. Find the final temperature of water, if the specific heat of water `= 4.18g^(-1)K^(-1)`.

Explanation

Work done by the system,
`w =P DeltaV =P (V_(2)-V_(1))`
`=3.0 (5-3) = 6L atm`
or `w = 6 xx 101.3J = 607.8 J ( :' 1L atm = 101.3J)`
This work is used for heating water.
Molar heat capacity of water `= 4.184 xx 8`
`75.312 J K^(-1) mol^(-1)`
Now, `Q = mst`
`607.8 = 10 xx 75.312 xx t or t = 0.81 K`
`:.` Final temperature of water `=290 +0.81 = 290.81K`.