During an adiabatic expansion of a monatomic gas, a 3% increase in the volume of the gas will produce a decrease in the temperature (absolute) of the gas of

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For an adiabatic process involving a monatomic gas, the relationship between volume (V) and temperature (T) is given by $TV^{\gamma-1} = \text{constant}$, where $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$ for a monatomic gas. A 3% increase in volume (i.e., $V$ becomes 1.03$V$) implies $T$ must decrease to maintain the constant, and the decrease in $T$ can be calculated using the relationship $T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1}$. Substituting $\gamma = \frac{5}{3}$ and solving for the percentage change in $T$ yields approximately a 2% decrease.

During an Adiabatic Expansion of a Monatomic Gas, a 3