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An ideal gas undergoes isothermal compre...

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

A

`(3)/(2)K`

B

2K

C

1K

D

`(2)/(3)K`

Text Solution

Verified by Experts

The correct Answer is:
D
`V_(i)=5m^(3)`
`V_(f)=1m^(3)`
`P_("ext")=4N//m^(2)`
Isothermal `to Delta U=0`
`q+W=0`
`q= -W= -[- int P_("ext")dV]=int P_("ext")dV=P_("ext")int dV=P_("ext")DeltaV=4[1-5]=4xx(-4)=-16J`
Heat lost by the system = 16J
`16=nCDeltaT`
`16=(1)(24)DeltaT`
`DeltaT=(16)/(24)=(2)/(3)`
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