2L of an ideal gas at a pressure of 10 atm expands isothermally into a vacuum until its total volume is 10L.
(i) How much heat is absorbed and how much work is done in the expansion?
(ii)How much heat is absorbed if this system expands againts a constant external pressure of 1 atm?
(iii) How much heat is absorbed if the expansion is conducted reversibly at 298 K.

Explanation

When the system is conducted isothermally, `DeltaU = 0`
so that `q = -w = p_(ex)DeltaV = p_(ex)(10 -2)`
`= 0 xx 8 = 0`
`because` expansion occurs in vaccum, `p_(ex) = 0`
No work is done, no heat is absorbed
(ii)`q = -w = p_(ex)(8) = 1 atm xx 8L = 8L` atm
or `= 8 xx 101.3 J = 810.4`J
(iii) `q = -w = 2.303` nRT `log ((V_(2))/((V_(1)))`
` = 2.303 pV log ((V_(2))/(V_(1)))`
` = 2.303 xx 10 atm xx 2L log ((10)/(2))`
`= 2.303 xx 10 atm xx 2L xx 0.699`
` = 32.2` L atm.
` = 32.2 xx 101.3 J = 3262.1 J = 3.26` kJ.