Question

the volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. By what factor does the temperature increase?

Answer 1

Due compression pressure heat is generated

Answer 2

1.32.

In an adiabatic system we have PV = constant. Hence, P1V1 = P2V2.

Therefore, V1/V2 = P2/P1. We also have P2 = 2.5P1, V2 =V1/2.

Putting these values in proper order, we get 2 to the power y is equal to 2.5.

That comes to the conclusion y = 1.32.

An adiabatic process takes place without any transfer of mass or heat from an item between its thermodynamic system and that of its surroundings.

The energy is transferred here only as work.