`1` mole of an ideal diatomic gas undergoes a reversible polytropic process `(PV^(2)="constant")`. The gas expand from initial volume of `1` litre and temp `300 K` to final volume `3` lit. Claculate change in internal energy (approx).

Options

A. `-40 KJ`
B. `-4.2 KJ`
C. `-4.4 KJ`
D. `-4.6 KJ`

Answer

B

Explanation

For polydropic process `(n=2)`
`PV^(2)=C`
`TV=C`
`T_(1)V_(1)=T_(2)V_(2)`
`300xx1=T_(2)xx3 rArrT_(2)=100 K`
` Delta U=nC_(v,m)Delta T=1xx(fR)/(2)(T_(2)-T_(1))=1xx(5xxR)/(2)xx(100-300)=(1xx5xxR)/(2)xx200= -500 R= -4.2 KJ`