2.50 mole sample of an ideal gas, for which , is subjected to two successive changes in state: (1) from 25.0°c and , the gas is expanded isothermally against a constant pressure of to twice the initial volume. (2) at the end of the previous process, the gas is cooled at constant volume from 25.0°c to –29.0°c. calculate q, w, , and for each of the stages. also calculate q, w, , and for the complete process

(1) W = - 4293.3 J; Q = 4293.3 J

(2) W = 0 J; Q = - 1683.585 J

(3) Wt = -4293.3 J; Qt = 2609.72 J

Explanation:

(1) ΔU = 0

⇒ Q = - W

⇒ W = - ∫PdV

∴P = nRT/V

⇒ W = - nRT ∫dV/V

⇒ W = - nRT Ln (Vf/Vi) = - nRT Ln(2Vi/Vi) = - nRT Ln(2)

⇒ W = - (2.5)(8.314)(298)(0.693) = - 4293.3 J

⇒ Q = 4293.3 J

(2) W = 0

⇒ ΔU = Q = Cv*ΔT

∴ ΔT = 244 - 298 = - 54K

∴ Cv = 1.5*R = 12.471 J/mol.K

⇒ Q = (12.471)*(- 54)*(2.5) = - 1683.585 J

(3) ⇒ Wt = W(1) + W(2) = -4293.3 + 0 = - 4293.3 J

⇒ Qt = Q(1) + Q(2) = 4293.3 - 1683.585 = 2609.72 J

explanation:

two years ago, when picking flowers in the mountains back of yosemite valley, i found a book. it was blotted and storm-beaten; all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however; many of the inner pages were well preserved. and although all were more or less stained and torn, whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today; its granite pages have been torn and blurred by the same storms that wasted the castaway book.

two years ago, when picking flowers in the mountains back of yosemite valley; i found a book. it was blotted and storm-beaten, all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however, many of the inner pages were well preserved. and although all were more or less stained and torn; whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today, its granite pages have been torn and blurred by the same storms that wasted the castaway book.