TS EAMCET · Physics · Thermodynamics
An ideal gas having initial pressure \(\mathrm{P}\), volume \(\mathrm{V}\) and temperature \(\mathrm{T}\) is allowed to expand adiabatically until its volume becomes \(4 \mathrm{~V}\), while its temperature falls to \(\frac{\mathrm{T}}{2}\). If the work done by the gas during the expansion is \(\alpha \mathrm{PV}\), the value of \(\alpha\) is
- A 1.25
- B 1
- C 1.5
- D 2
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
For adiabatically process \[ \begin{array}{ll} \mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_2 \mathrm{~V}_2^{\gamma-1} & \\ \mathrm{TV}^{\gamma-1}=\frac{\mathrm{T}}{2}(4 \mathrm{~V})^{\gamma-1} & \\ 2=(2)^{2 \gamma-2} & \gamma=\frac{3}{2} \\ 2 \gamma-2=1 & \end{array} \]…
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