A heat insulating cylinder with a movable piston contains 5 moles of hydrogen at standard temperature and pressure if the gas is compressed to quarter of its original volume then the pressure of the gas is increased by `(gamma=1.4)`

Options

A. `(2)^(1.4)`
B. `(3)^(1.4)`
C. `(4)^(1.4)`
D. `(5)^(1.4)`

Answer

C

Explanation

As the cylinder is a heat insulating i.e no heat is allowed to be exchanged .Hence the process is adiabatic
`P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
`(P_(2))/(P_(1))=(V_(1))/(V_(2))^(gamma)`
Here `V_(1)=V,V_(2)=(V)/(4),P_(1)=P` and `gamma=1.4`
`(P_(2))/(P)=((V)/(V//4))^(1.4)=(4)^(1.4) rArr P_(2)=(4)^(1.4)P`