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Heat and Thermodynamics question

2019 · 12 Jan · Shift 2 · Q53
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  5. /2019 · 12 Jan · Shift 2 · Q53

Heat and Thermodynamics question

2019 · 12 Jan · Shift 2 · Q53

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is ℓ\ellℓ 1, and that below the piston is ℓ\ellℓ 2, such that ℓ\ellℓ 1 > ℓ\ellℓ 2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)
  1. A
    nRTg[ℓ1−ℓ2ℓ1ℓ2]{{nRT} \over g}\left[ {{{{\ell _1} - {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]gnRT​[ℓ1​ℓ2​ℓ1​−ℓ2​​]
  2. B
    RTg[2ℓ1+ℓ2ℓ1ℓ2]{{RT} \over g}\left[ {{{2{\ell _1} + {\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]gRT​[ℓ1​ℓ2​2ℓ1​+ℓ2​​]
  3. C
    nRTg[1ℓ2+1ℓ1]{{nRT} \over g}\left[ {{1 \over {{\ell _2}}} + {1 \over {{\ell _1}}}} \right]gnRT​[ℓ2​1​+ℓ1​1​]
  4. D
    RTng[ℓ1−3ℓ2ℓ1ℓ2]{{RT} \over {ng}}\left[ {{{{\ell _1} - 3{\ell _2}} \over {{\ell _1}{\ell _2}}}} \right]ngRT​[ℓ1​ℓ2​ℓ1​−3ℓ2​​]
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