The relation between absolute temperature $(\mathrm{T})$ and pressure (P) of a gas in an adiabatic process is

The relation between absolute temperature $(\mathrm{T})$ and pressure (P) of a gas in an adiabatic process is
  1. $\mathrm{p}^{\mathrm{g}} \mathrm{T}^{1-\mathrm{g}}=$ constant
  2. $\mathrm{p}^{1-\mathrm{g}} \mathrm{T}^{\mathrm{g}}=$ constant
  3. $\mathrm{p}^{\mathrm{g}-1} \mathrm{~T}^{\mathrm{g}}=$ constant
  4. $\mathrm{p}^{\mathrm{g}} \mathrm{T}^{\mathrm{g}-1}=$ constant

Solution

The relation between temperature and pressure is given by $\begin{aligned} & \mathrm{PV} \gamma=\text { constant }(\mathrm{PV}=\mathrm{nRT}) \\ & \Rightarrow \mathrm{V}=\frac{\mathrm{nRT}}{\mathrm{P}} \\ & \Rightarrow \mathrm{p}\left(\frac{\mathrm{nRT}}{\mathrm{p}}\right)^\gamma=\text { constant } \\ & \mathrm{p}^{1-\gamma} \mathrm{T}^\gamma=\text { constant }\end{aligned}$

Asked in: AP EAMCET 2023 (17 May Shift 2)

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