An ideal gas () is used in a Carnot cycle as a working substance. The efficiency of the cycle, if as — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

For adiabatic expansion in the Carnot cycle: $\frac{T_1}{T_2} = \left(\frac{V_2}{V_1}\right)^{\gamma-1} = (2.75)^{0.4}$. Using the hint, $2.75^{0.4} = ((1.5)^{2.5})^{0.4} = 1.5$. Thus $\frac{T_2}{T_1} = \frac{1}{1.5} = \frac{2}{3}$. Efficiency $\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{2}{3} = \frac{1}{3} = 33.33\% = \frac{100}{3}\%$.