Which of the following is true in the case of an adiabatic process, where $\gamma=C_p / C_V$ ?

Which of the following is true in the case of an adiabatic process, where $\gamma=C_p / C_V$ ?
  1. $p^{1-\gamma} T^\gamma=$ constant
  2. $p^\gamma T^{1-\gamma}=$ constant
  3. $p T^\gamma=$ constant
  4. $p^\gamma T=$ constant

Solution

For adiabatic change equation of state is $ p V^\gamma=\text { constant } $ It can also be re-written as $ T V^{\gamma-1}=\text { constant }\left[\text { as } p=\frac{n R T}{V}\right] $ and $\quad p^{1-\gamma} T^\gamma=$ constant $\left[\right.$ as $\left.V=\frac{n R T}{p}\right]$

Asked in: AP EAMCET 2008

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