Question

In an adiabatic process for an ideal diatomic gas, the volume of the gas doubles. If the temperature starts at 40°C, what is the final temperature, Tf in °C?

Answer 1

Question 24595

Equation of adiabatic process is $T V^{k-1} = \text{const}$ , where $k$ is constant, which depends on type of gas.

By definition $k = \frac{C_p}{C_v}$ , where $C_p$ is heat capacity for constant pressure and $C_v$ is heat capacity for constant volume. $k$ might be expressed in terms of number of degrees of freedom $s: k = \frac{s + 2}{s}$ . For diatomic gas, $s$ is equal to 5, hence $k = 7/5$ .

Hence, $T_{1}V_{1}^{\frac{2}{5}} = T_{2}\cdot 2^{\frac{2}{5}}V_{1}^{\frac{2}{5}}\Rightarrow T_{2} = \frac{T_{1}}{2^{\frac{2}{5}}}\approx 30.31\deg$