During an experiment, an ideal gas is found to obey an additional law `VP^2=constant,` The gas is initially at a temperature T, and volume V. When it expands to a volume `2V,` the temperature becomes…….

Options

A. `sqrt3T`
B. `sqrt(1//2T)`
C. `Tsqrt2`
D. `sqrt(3T)`

Answer

C

Explanation

Here, It is given that `VP^(2)` = constant K (say). Hence , we may write the gas equation as ,
pV=nRT
`P=sqrt((K)/(V))" or " sqrt((K)/(V)).V=nRT`
`"or "sqrtV=(nR)/(sqrtK)T rArr sqrt((V_(1))/(V_(2)))=(T_(1))/(T_(2))`
`therefore" "T_(2)=T_(1)sqrt((V_(2))/(V_(1)))=Tsqrt((2V)/(V))=Tsqrt2`