WBJEE · Physics · Thermodynamics
One mole of an ideal monoatomic gas expands along the polytrope \(PV^3=\) constant from \(V_1\) to \(V_2\) at a constant pressure \(P_1\). The temperature during the process is such that molar specific heat \(C_V=\frac{3 R}{2}\). The total heat absorbed during the process can be expressed as
- A \(\quad P_1 V_1\left(\frac{V_1^2}{V_2^2}+1\right)\)
- B \(\mathrm{P}_1 \mathrm{~V}_1\left(\frac{\mathrm{V}_1^2}{\mathrm{~V}_2^2}-1\right)\)
- C \(\mathrm{P}_1 \mathrm{~V}_1\left(\frac{\mathrm{V}_1^3}{\mathrm{~V}_2^2}-1\right)\)
- D \(\quad P_1 V_1\left(\frac{V_1}{V_2^2}-1\right)\)
Answer & Solution
Correct Answer
(B) \(\mathrm{P}_1 \mathrm{~V}_1\left(\frac{\mathrm{V}_1^2}{\mathrm{~V}_2^2}-1\right)\)
Step-by-step Solution
Detailed explanation
Assuming \(P_1\) as initial pressure. \(\mathrm{PV}^3=\) constant \(n=3\) \[ \mathrm{C}=\mathrm{C}_{\mathrm{V}}+\frac{\mathrm{R}}{1-\mathrm{n}}=\frac{3 \mathrm{R}}{2}+\frac{\mathrm{R}}{1-3}=\mathrm{R} \]…
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