When 3mole of an idela gas expand reversibly and isothermally five times its initial volume `6kJ` heat flow into it. What must be the temperature of the gas?

Explanation

`V_(1) = V, V_(2) = 5V`
`q = 6 kJ, n = 3`
Since temperature is constant
`:. DeltaU = 0, DeltaU = q +w`
`:. Q =- w`
`w_("rev'isothermally")`
`=- nRT xx 2.303 log.(V_(2))/(V_(1))`
`= 3xx2.314 xx 2.303 log. (5V)/(V) xxT`
`w =- 40.208T`
`:. q = 6kJ = 6 xx 10^(3)J`
`q =- w`
`6 xx 10^(3) = 40.208T`
`T = 149.4K`.