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Homework Statement
An ideal Brayton cycle has a pressure ratio of 15 and can be analysed using air standard cycle assumptions. The gas temperature is 300K at the compressor inlet and 1500K at the turbine inlet.
The compressor and turbine can be considered to be isentropic.
For an isentropic process,[tex]pv^{\gamma}[/tex] = constant.
Work out the temperature at the end of the compressor.
Homework Equations
[tex]P_{1}[/tex] [tex]V_{1}^{\gamma}[/tex] = [tex]P_{2}[/tex][tex]V_{2}^ {\gamma}[/tex]
[tex]P_{1}[/tex] [tex]V_{1}[/tex] = [tex]R T_{1}[/tex]
[tex]P_{2}[/tex] [tex]V_{2}[/tex] = [tex]R T_{2}[/tex]
The Attempt at a Solution
I've sketched the cycle on a ts property diagram to illustrate the problem.
From the relevant equations, I have that:
[tex]T_{2} = T_{1}(\frac{P_{2}}{P_{1}})^{\gamma  1/ \gamma}[/tex]
Which gives me, [tex]T_{2} = 300.15^{\gamma  1/ \gamma}[/tex]
I have [tex]T_{1}[/tex] = 300 and the pressure ratio = 15 but I see no way to complete the equation as I don't know the heat capacity ratio, [tex]{\gamma}[/tex] or a way to work it out.
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