Verified Solution • 2025–26 Session moderate

QJEEM22Phe871: JEE Main 2022 Physics - Class 11 JEEM22Phe871 Solution: A thermally insulated vessel contains an ideal gas of molecular …

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :

(R = universal gas constant)

Multiple Choice Options

  • A Mv27R{{M{v^2}} \over {7R}}
  • B Mv25R{{M{v^2}} \over {5R}}
  • C 2 Mv27R{{M{v^2}} \over {7R}}
  • D 7 Mv25R{{M{v^2}} \over {5R}}

Step-by-Step Verified Solution

Let there be n moles of gas

Eloss = Egain

12(nM)v2=nCvΔT{1 \over 2}(nM){v^2} = n{C_v}\Delta T

12Mv2=CvΔT{1 \over 2}M{v^2} = {C_v}\Delta T

here, γ=1.4=75\gamma = 1.4 = {7 \over 5} i.e. diatomic gas

∴\therefore Cv=5R2{C_v} = {{5R} \over 2}

Now, 12Mv2=5R2ΔT{1 \over 2}M{v^2} = {{5R} \over 2}\Delta T

ΔT=Mv25R\Delta T = {{M{v^2}} \over {5R}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring