Two litresof an ideal gas at a pressure of 10 atmexpands Isothermally into vacuum until its total volumeis 10 litres. How muach heat is absorbed and howmuch work is done in the expansion ?What would be the heatabsorbed andwork done (i) if the same expansion takes place against a constant external pressureof 1 atm ? (ii) if the same expansion takes place to a final volume of 10 litres conducted reversibly?

Two litresof an ideal gas at a pressure of 10 atmexpands Isothermally

1.	Two litresof an ideal gas at a pressure of 10 atmexpands Isothermally into vacuum until its total volumeis 10 litres. How muach heat is absorbed and howmuch work is done in the expansion ?What would be the heatabsorbed andwork done (i) if the same expansion takes place against a constant external pressureof 1 atm ? (ii) if the same expansion takes place to a final volume of 10 litres conducted reversibly?
Answer» Solution :For isothermal expansion of an ideal gas,` Delta U = 0` `:. q = -w= P_(ext) ( 10L-2L) = 0 (8) = 0` (i) ` q= - w = 1 ATM xx 8 L = 8 L atm = 8 xx 101.3 J = 810.4 J ( 1L atm = 101. 3 J )` (ii) `q= -w= 2.303 RT log. (V_(2))/(V_(1)) = 2.303 PV log . (V_(2))/(V_(1)) = 2.303 xx 10 atm xx 2 L log. (10)/(2) = 32. 2 L atm.` `= 32.2 xx 101 . 3 J = 3261.86J`