Work done in expansion of an idela gas from `4L` to `6L` against a constant external pressure of `2.5 atm` was used to heat up `1mol` of water at `293K`. If specific heat of water is `4.184J g^(-1)K^(-1)`, what is the final temperature of water.

Options

A. 300K
B. 456 K
C. 278 K
D. 600 K

Answer

A

Explanation

Since, work is done against constant pressure process is irreversible.
Given, `Delta V = (6-4) = 2` litre, p = 2.5 atm
`w = -p_(ext) xx Delta V = -2.5 xx 2 = -5` litre-atm
`= - (5 xx 1.987)/(0.0821)cal = (5 xx 1.987 xx 4.187)/(0.0821)J = -506.31 J`
`C = 4.184J//g//K` or `4.184J//mol`
Now this work is used in heating 1 mole water
`W = n xx C xx Delta T 506.31`
`= 1 xx 4.184 xx Delta T :. Delta T = 6.723`
Final temp `= T_(1) + Delta T = 293 +6.723 = 299.723 K`