Q111 / 180 · NEET 2013 (Karnataka) · 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
    $\mathrm{PV}=$ constant
  • C
    $T W^{-1}=$ constant
  • Correct answer
    D
    $P^{\prime} T^{1-\gamma}=$ constant

Solution

Adiabatic process $\rightarrow$ Heat does not exchange between system surrounding and eq. is $\mathrm{PV}^\gamma=$ constant Ideal gas $P V=n R T$ $P=\frac{n R T}{V}=\frac{n R T}{V} \quad \mathrm{~V}^\gamma=$ const $\mathrm{TV}^{\gamma-1}=$ constant Again $\quad P V=n R T$ $V=\frac{n R T}{P}$ Pulley in eq. (i) $P\left(\frac{n R T}{P}\right)^\gamma=$ constant $P^{1-\gamma} \mathrm{T}^\gamma=$ constant...(iii) So, option (d) does not give the relation.

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

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