An ideal gas undergoes isothermal compression from `5 m^(3)` to `1 m^(3)` against a constant external pressure of `4Nm^(-2)`. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J `mol^(-1)K^(-1)`, the temperature of Al increases by

Options

A. `32 K`
B. 2K
C. 1K
D. `2/3` K

Answer

D

Explanation

`V_(1) = 5m^(-1), V_(f) = 1m^(3)`
`P_(ext) = 4N//m^(2)`
Isothermal `to DeltaU=0`
q+W=0
`q=-W = -[-intP_(ext)dV] = intP_(ext)dV =P_(ext)int dV = P_(ext) DeltaV = 4[1-5] = 4 xx (-4) = -16 J`
Heat lost by the system = 16 J
16= `nCDeltaT`
`16=(1)(24)DeltaT rArr DeltaT = 16/24 = 2/3`