Question

One mole of an ideal monoatomic gas at temperature `T_(0)` expands slowely according to the law P/V=constant. If the final temperature is `2T_(0)` heat supplied to the gas is -
A. `2RT_(0)`
B. `3/2RT_(0)`
C. `RT_(0)`
D. `1/2RT_(0)`

Answer 1

Correct Answer - 1
`P/V`=consatnt, PV=RT
W=`intPdV=C overset(V_(2))underset(V_(2))intVdV`
`W=C[V^(2)/2]`
`=1/2P_(2)V_(2)-(P_(1)V_(1))/2`
`=1/2R(T_(2)-T_(1))`
`=1/2RT_(0)`
`DeltaU=1xx3/2RxxT_(0)`
`=3/2RT_(0)`
`Q=W+DeltaU=2 RT_(0)`