Where y = Cp/Cv. Find a similar equation that relates temperature and pressure o

Question

Where y = Cp/Cv. Find a similar equation that relates temperature and pressure of an ideal gas during a reversible adiabatic process. Similarly, an irreversible adiabatic process can be described with C_v Delta T = -p_ext Delta V, which leads to an equation: which solves for the final volume given the heat capacity ratio y, initial volume, and the initial and final pressures (and assuming p2 = p_ext). Find an analogous expression that relates the final temperature of an ideal gas during an irreversible adiabatic process to its initial temperature, the heat capacity ratio, and the initial and final pressures. Let s do some calculations on gas cylinders-one reasonable and one terribly dangerous. For

Explanation / Answer

A similar equation that relates temperature and pressure of an ideal gas during a reversible adiabatic process,
P1-T = constant or
(P1 / P2)1- = (T2 / T1)   
An analogous expression that relates final temperature of an ideal gas during an irreversible adiabatic process
to its initial temperature, the heat capacity ratio and the initial and final pressures.
T2 = [ (Cv + (P2 / P1) ) / Cp ] * T1

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