Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20248 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Morning Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2024 · 8 April · Morning Shift · Physics · Thermodynamics

Two different adiabatic paths for the same gas intersect two...

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio VaVd\frac{V_a}{V_d} and the ratio VbVc\frac{V_b}{V_c} is: Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation

Options

  1. AVaVd≠VbVc\frac{V_a}{V_d} \neq \frac{V_b}{V_c}
  2. BVaVd=VbVc\frac{V_a}{V_d}=\frac{V_b}{V_c}
  3. C\frac{V_a}{V_d}=(VbVc)−1\left(\frac{V_b}{V_c}\right)^{-1}
  4. DVaVd=(VbVc)2\frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^2

Correct answer

B. VaVd=VbVc\frac{V_a}{V_d}=\frac{V_b}{V_c}

Step-by-step solution

For adiabatic process TVγ−1=\mathrm{TV}^{\gamma-1}= constant Ta⋅Vaγ−1=Td⋅Vdγ−1(VaVd)γ−1=TdTaTb⋅Vbγ−1=Tc⋅Vcγ−1(VbVc)γ−1=TcTbVaVd=VbVc(∵Td=TcTa=Tb)\begin{aligned} & \mathrm{T}_{\mathrm{a}} \cdot \mathrm{V}_{\mathrm{a}}^{\gamma-1}=\mathrm{T}_{\mathrm{d}} \cdot \mathrm{V}_{\mathrm{d}}^{\gamma-1} \\ & \left(\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{d}}}\right)^{\gamma-1}=\frac{\mathrm{T}_{\mathrm{d}}}{\mathrm{T}_{\mathrm{a}}} \\ & \mathrm{T}_{\mathrm{b}} \cdot \mathrm{V}_{\mathrm{b}}^{\gamma-1}=\mathrm{T}_{\mathrm{c}} \cdot \mathrm{V}_{\mathrm{c}}^{\gamma-1} \\ & \left(\frac{\mathrm{V}_{\mathrm{b}}}{\mathrm{V}_{\mathrm{c}}}\right)^{\gamma-1}=\frac{\mathrm{T}_{\mathrm{c}}}{\mathrm{T}_{\mathrm{b}}} \\ & \frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{d}}}=\frac{\mathrm{V}_{\mathrm{b}}}{\mathrm{V}_{\mathrm{c}}} \quad\left(\begin{array}{c}\because \mathrm{T}_{\mathrm{d}}=\mathrm{T}_{\mathrm{c}} \\ \mathrm{T}_{\mathrm{a}}=\mathrm{T}_{\mathrm{b}}\end{array}\right)\end{aligned}
Practice Thermodynamics on Quantrex Academy →

More from Thermodynamics

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( ab )… JEE Advanced 2026As shown in the figure, five Carnot engines, each with efficiency η and same number of… JEE Advanced 2026Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and… JEE Advanced 2026One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston… JEE Main 2026Initial pressure and volume of a monoatomic ideal gas are P and V . The change in… JEE Main 2026A cylinder with adiabatic walls is closed at both ends and is divided into two… JEE Main 2026Two closed vessels of same volume are joined through a narrow tube and both vessels are… JEE Main 2026A certain gas is isothermally compressed to ((1)/(3))^ rd of its initial volume ( V_o = 3… JEE Main 2026 Full Thermodynamics list All JEE Main PYQs