Q139 / 160 · TS EAMCET 2022 (20 Jul Shift 1) · Physics

When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor of 2 . The value of the adiabatic constant is

  • A
    1
  • B
    5/3
  • Correct answer
    C
    2
  • D
    7/5

Solution

For adiabatic process $\mathrm{TV}^{\gamma-1}=$ constant $$ \begin{aligned} & \Rightarrow \quad \mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_2 \mathrm{~V}_2^{\gamma-1} \Rightarrow \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right)^{\gamma-1} \\ & \Rightarrow \quad \frac{2 \mathrm{~T}}{\mathrm{~T}^{\prime}}=2^{\gamma-1} \Rightarrow 2^{\prime}=2^{\gamma-1} \Rightarrow 1=\gamma-1 \Rightarrow \gamma=2 \end{aligned} $$

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

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