Q156 / 180 · COMEDK 2013 · Physics

Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning?

  • A
    $p^{1-\gamma} T^{\gamma}=$ constant
  • B
    $p V^{\gamma}=$ constant
  • C
    $T V^{\gamma-1}=$ constant
  • Correct answer
    D
    $p^{\gamma} T^{1-\gamma}=\mathrm{constant}$

Solution

For adiabatic process, $p V^{\gamma}=$ constant For an ideal gas, $p V=n R T$ or $p=\frac{n R T}{V}$ Again, from ideal gas equation, $$ \begin{aligned} V &=\frac{n R T}{p} \\ \Rightarrow \quad p\left(\frac{n R T}{p}\right)^{\gamma} &=\text { constant } \\ \Rightarrow \quad p^{1-\gamma} T^{\gamma} &=\text { constant } \end{aligned} $$ Hence, relation shown in option (d) is not for adiabatic process.

Hence, the correct answer is option: 'D'.

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