Question

A gas is compressed by an adiabatic process that decreases its volume by a factor of 2.

In this process, the pressure

In this process, the pressure

a)	increases by a factor of more than 2.
b)	increases by a factor of 2.
c)	does not change.
d)	increases by a factor of less than 2.

Answer 1

The condition when the gas compressed adiabatically is, \(P V^{\gamma}=\) constant

\(P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}\)

\(P_{2}=\frac{P_{1} V_{1}^{\gamma}}{V_{2}^{\gamma}}\)

The pressure is, \(P_{2}=\frac{P_{1} V_{1}^{\gamma}}{\left(\frac{V_{1}}{2}\right)^{\gamma}}=2^{\gamma} P_{1}\)

Therefore, the pressure increases by a factor more than \(2 .\) Therefore, the correct option is (a).