An ideal monoatomic gas at 300   K expands adiabatically to twice its volume. The final temperature of gas is

Question

An ideal monoatomic gas at 300 &#160; K expands adiabatically to twice its volume. The final temperature of gas is

Aicharya · Accepted Answer

For an ideal monatomic gas, the ratio of specific heat capacity at constant pressure to specific heat capacity at constant volume is

$γ = \frac{5}{3}$

In an adiabatic process,

$T V^{γ - 1} =$ constant

i.e. $T_{f} V_{f}^{γ - 1} = T_{i} V_{i}^{γ - 1} \Rightarrow T_{f} = T_{i} {(\frac{V_{i}}{V_{f}})}^{γ - 1} = 300 {(\frac{1}{2})}^{\frac{5}{3} - 1}$

$= 300 {(\frac{1}{2})}^{2 / 3}$

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An ideal monoatomic gas at 300   K expands adiabatically to twice its volume. The final temperature of…