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Question

A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent γ moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

A
(γ1)Mv24R
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B
γMv22R
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C
Mv22(γ1)R
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D
(γ1)Mv22R
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Solution

The correct option is D (γ1)Mv22R

Kinetic energy of molecules is given by 12nMv2

Relation between cv and internal energy Uis given by

U=ncvΔT

cv=UnΔT........(1)

cpcv1=λ1

cpcvcv=λ1

Rcv=λ1

cv=Rλ1........(2)

From (1) and (2)UnΔT=Rλ1

U=RnΔTλ1

Now the internal energy is equal to the change in KE

RnΔTλ1=12nMv2

RΔTλ1=12nMv2

ΔT=Mv22R(λ1)If the box suddenly stops, then change in temperature of gas will be ΔT=Mv22R(λ1)


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