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)`.

Options

A. `290.2K`
B. `290.8K`
C. `298.0K`
D. `293.7K`

Answer

B

Explanation

Work done in expansion
`= PxxV = 3xx(5-3) = 6L-atm`
We have `1L-atm = 101.3J`
Work done `=6 xx 101.3J = 607.8J`
Let `DeltaT` be the change in temperature of water.
`:. P Delta V = mxxs xx Delta T`
`607.8 = 180 xx 4.184 xx DeltaT (m = mol xx Mw = 10 xx 18 = 180)`
`DeltaT = 0.81K`
`T_(f) = T_(i) +DeltaT = 290.0K`