I am reading through my thermodynamics book. Going over a air-standard otto cycle example problem. For reference the example problem is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

The temperature at the beginning of the compression process of an air-standard Otto cycle with a compression

ratio of 8 is 5408R, the pressure is 1 atm, and the cylinder volume is 0.02 ft3. The maximum temperature during

the cycle is 36008R. Determine (a) the temperature and pressure at the end of each process of the cycle, (b) the

thermal efficiency, and (c) the mean effective pressure, in atm.

After finding the values for u_{1}and v_{r1}from a table and using the air-standard relation of v_{r2}=(V_{2}/V_{1})(v_{r1}) which I followed. Then using that to interpolate a value for T_{2}and u_{2}, the solution then states that since process 2-3 occurs at constant volume we can find p_{2}by the following equation:

p_{2}= p_{1}((T_{2}/T_{1})(V_{1}/V_{2}))

I'm trying to understand where this is coming from because I don't see this on any ideal gas tables. I'm sure I'm missing some simple relation but if anyone can help explain where this relation has come from and why we can use it I would appreciate it.

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# Help with Ideal gas equation of state

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