Two moles of an idela gas at `2atm` and `27^(@)C` is compressed isothermally to one-half of its volume by an external pressure of `4atm`. Calculate `q,w`, and `DeltaU`.

Explanation

Work done on the system,
`w =- p DeltaV =- (V_(f)-V_(i))`
`p = 4 atm, V_(i) = (nRT)/(p)`
`n = 2 mol R = 0.082 atm L mol^(-1) K^(-1)`,
`T = 273 +27 = 300K,p = 2 atm`
`V_(i) = (2xx 0.082 xx 300)/(2) = 24.6L`
and `V_(f) = (V_(i))/(2) = (24.6)/(2) = 12.3L`
`w =- 4 atm xx (12.3 - 24.6)L`
`= 49.2 L-atm = 49.2 xx 101.3 J = 4984J`.
Since, it is isothermal compression, `DeltaU = 0`
Now, `DeltaU = q +w`
`0 = q + 4984J`
or `q =- 4984 J`