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

Answer

B

Explanation

For osothermal irreversible compression of an ideal gas,
`w = -p_(ext)(V_(2)-V_(1))`
` = -4Nm^(-2)(1 - 5) m^(3)`
= 16Nm
For isothermal process
`DeltaU = q + w or 0 = q + w`
`q = -w = -16Nm = -16J`
Heat is used to increase the temperature of AI,
`q = nC_(m) DeltaT`
`16J = 1 xx 24 J "mol"^(-1) K^(-1) xx DeltaT`
or `DeltaT = 16/24 or DeltaT = 2/3K`.