    Question

# An adiabatic piston of mass m equally divides a diathermic container of volume V0 and length l. A light spring connects the piston to the right wall. At equilibrium, pressure on each side of the piston is P0. The container starts moving with acceleration a towards the right. Then, Assume that x<<l, the gas in the container has the adiabatic exponent (ratio of CP and CV)γ, m=2 kg, a=2 m/s2 A
The piston will move with acceleration a at equilibrium.
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B
The stretch x of the spring when the acceleration of the piston equals the acceleration of the container is mak+2P0γAl.
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C
The difference in pressure between the two compartments is 4P0γAl
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D
The stretch x of the spring when the acceleration of the piston equals the acceleration of the container is mak+4P0γAl.
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Solution

## The correct options are A The piston will move with acceleration a at equilibrium. C The difference in pressure between the two compartments is 4P0γAl D The stretch x of the spring when the acceleration of the piston equals the acceleration of the container is mak+4P0γAl. Drawing F.B.D of piston. P1A+kx−P2A=ma---(i) If the spring is stretched by a distance x, V1=A(l2−x) V2=A(l2+x) V0=Al2 Since the process is adiabatic, P0Vγ0=P1Vγ1=P2Vγ2 ⇒P1=P0(V0V1)γ=P0(ll−2x)γ ⇒P1=P0(1−2xl)−γ ⇒P1=P0(1+2γxl) ---- (ii) (using binomial expansion ∵ x<<l) Similarly P2=P0(1+2xl)−γ =P0(1−2γxl) --- (iii) Substituting (ii) and (iii) in (i), (P1−P2)A+kx=ma 4P0γxAl+kx=ma ⇒x=mak+4P0γAl=4k+4P0γAl ∴n=4  Suggest Corrections  1      Explore more