# Differential Equations : Thermodynamics of an Ideal Gas and Small Stage Efficiency

1. For a thermodynamic process involving a perfect gas, the intial and final temperatures are related by:

where is the specific heat capacity of the gas, is the change of entropy and and are the initial and final temperatures of the process. Determine the value of if and .

2. The overall efficiency of a gas turbine can be calculated from the formula

where is the small stage efficiency and , where r is the expansion pressure ratio and is the ratio of the specific heats. Given that the overall efficiency is 76%, , calculate the value of the small stage efficiency .

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Differential Equations, Thermodynamics of an Ideal Gas and Small Stage Efficiency are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.