First slide

Different type of processes

Question

At 27°C two moles of an ideal gas $(γ = 3 / 2)$ occupy a volume V. The gas expands adiabatically to a volume 2V. Final temperature of the gas approximately is

Moderate

A

189 K
B

212 K
C

248 K
D

179 K

Solution

Here $V_{1} = V, V_{2} = 2 V, T_{1} = 300 K$
Adiabatic relation $TV^{γ - 1} = constant$
$\begin{array}{l} T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} \\ T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ - 1} = 300 {(\frac{1}{2})}^{1 / 2} \\ T_{2} = 212 K . \end{array}$

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