1 mole of an ideal gas in a cylindrical container have the P-V diagram as shown in figure.If `V_(2)=4V_(1)` then the ratio of temperatures `(T_(1))/(T_(2))` will be

Options

A. `1/2`
B. `1/4`
C. `3/2`
D. `3/4`

Answer

A

Explanation

Ideal gas equation PV=nRT ltnrgt or `T=(PV)/(nR)`
According to question
`PV^(1//2)="constant"(A)`
multipling both side by `sqrt(V)`
or `PV=Asqrt(V)`
Form eqn's (i) and (ii)
`T=(Asqrt(V))/(nR) rArr T prop sqrt(V)`
`Now (T_(1))/(T_(2))=sqrt(V_(1)/(V_(2))=sqrt(V_(1)/(4V_(1))=(1)/(2)`
`(T_(1))/(T_(2))=(1)/(2)`