An ideal gas ( γ = 1.5 ) undergoes an adiabatic change in volume from 4.00 litres to 3.00 litres. Determine the ratio of its final pressure to its initial pressure.

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Quantrex Academy · Accepted Answer

Correct answer: B. 1.54

For an adiabatic process, the equation of state is given by:

P_1 V_1^{\gamma} = P_2 V_2^{\gamma}

Rearranging for the ratio of final pressure to initial pressure:

\dfrac{P_2}{P_1} = \left(\dfrac{V_1}{V_2}\right)^{\gamma}

Substituting the given values

V_1 = 4.00

L,

V_2 = 3.00

L, and

\gamma = 1.5 = \dfrac{3}{2}

:

\dfrac{P_2}{P_1} = \left(\dfrac{4}{3}\right)^{3/2}

\dfrac{P_2}{P_1} = \dfrac{4^{3/2}}{3^{3/2}} = \dfrac{8}{3\sqrt{3}}

Using

\sqrt{3} \approx 1.732

:

\dfrac{P_2}{P_1} = \dfrac{8}{3 \times 1.732} = \dfrac{8}{5.196} \approx 1.54

An ideal gas ( γ = 1.5 ) undergoes an adiabatic change in volume...

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