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`.

Two moles of an idela gas at `2atm` and `27^(@)C` is compressed isothe

1.	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`.
Answer» 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`

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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`.

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