In ideal engine operates on the Carnot cycle using a perfect gas as the working fluid. The ratio of the greatest to the least volume is fixed and is x:1. The lower temperature of the cycle is also fixed, but the volume compression/expansion ratio ‘r’ of the reversible adiabatic compression is variable. The ratio of the specific heats is γ. Determine the work done per kg of air.
1
\(R{T_3}\left( {1 - {r^{\gamma - 1}}} \right)\ln \frac{x}{r}\)
2
\({\rm{R}}{{\rm{T}}_3}\left( {1 - {r^{r - 1}}} \right)\ln \frac{r}{x}\)
3
\(R{T_3}\left( {1 - \frac{1}{{{r^{r - 1}}}}} \right)\ln \frac{x}{r}\)
4
\(R{T_3}\left( {1 - \frac{1}{{{r^{r - 1}}}}} \right)\ln \frac{r}{x}\)