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 temperature to its initial temperature.

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Quantrex Academy · Accepted Answer

Correct answer: D. 1.15

For an adiabatic process, the relation between temperature and volume is given by:

T V^{\gamma - 1} = \text{constant}

Therefore,

T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}

Rearranging for the ratio of final to initial temperature:

\dfrac{T_2}{T_1} = \left(\dfrac{V_1}{V_2}\right)^{\gamma - 1}

Substituting the given values

V_1 = 4.00

L,

V_2 = 3.00

L, and

\gamma = 1.5

:

\dfrac{T_2}{T_1} = \left(\dfrac{4.00}{3.00}\right)^{1.5 - 1}

\dfrac{T_2}{T_1} = \left(\dfrac{4}{3}\right)^{0.5}

\dfrac{T_2}{T_1} = \sqrt{\dfrac{4}{3}} = \dfrac{2}{\sqrt{3}}

Using

\sqrt{3} \approx 1.732

:

\dfrac{T_2}{T_1} = \dfrac{2}{1.732} \approx 1.15

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

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