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0.5 mole of an ideal gas at constant tem...

`0.5` mole of an ideal gas at constant temperature `27^(@)C` kept inside a cylinder of length `L` and cross-section area A closed by a massless piston The cylinder is attached with a conducting rod of length `L` cross-section area `(1//9)m^(2)` and thermal conductivity k whise other end is maintained at `0^(@)C` If piston is moved such that rate of heat flow through the conducing rod is constant then find velocity of piston when it is at height `L//2` from the bottom of cylinder [Neglect any kind of heat loss from system
.

A

`(k)/(50R)`

B

`(k)/(100R)`

C

`(k)/(110R)`

D

`(k)/(90R)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(DeltaQ)/(Deltat) = (Deltaw)/(Deltat)` work done per unit time `= (ka theta)/(L)`
`"Power" = F xx "Velocity" = PAV' = (nRT)/(v) AV`
where `V rarr` volume `V' rarr` velocity
`rArr (0.5 R(300))/(V) AV' = (ka theta)/(L)`
`(0.5 R(300))/(A (L)/(2))AV' = (ka theta)/(L) rArr V' = (ka)/(R) ((27)/(300)) = (k)/(100R)` .
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Knowledge Check

  • 0.5 mole of an ideal gas at constant temperature 27^(@)C kept inside a cylinder of length L and crosssection area A closed by a massless piston The cylinder is attached with a conducting rod of length L , cross-section area (1/9) m^(2) and thermal conductivity k, whose other end is maintained at 0^(@)C . If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height L/2 from the bottom of cylinder is : [Neglect any kind of heat loss from system ]

    A
    `((k)/(R )) m//sec`
    B
    `((k)/( 10R )) m//sec`
    C
    `((k)/(100R)) m//sec`
    D
    `((k)/( 1000R)) m//sec`

  • A metal rod of area of cross section A has length L and coefficient of thermal conductivity K the thermal resistance of the rod is .

    A
    `(L)/(KA)`
    B
    `(KL)/(L)`
    C
    `(KA)/(L)`
    D
    `(A)/(KL)`

  • If l is the length, A is the area of cross-section and K the thermal conductivity, then the thermal resistance of the block is given by

    A
    `(Kl)/(A)`
    B
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    C
    `(AK)/(l)`
    D
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