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The specific heat capacity of a metal at...

The specific heat capacity of a metal at low temperature (T) is given as
`C_(p)(kJK^(-1) kg^(-1)) =32((T)/(400))^(3)`
A 100 gram vessel of this metal is to be cooled from `20^(@)K` to `4^(@)K` by a special refrigerator operating at room temperaturte `(27^(@)C)` . The amount of work required to cool the vessel is

A

greater than `0.148 kJ`

B

between `0.148 kJ` and `0.028 kJ`

C

less than `0.028 kJ`

D

equal to `0.002 kJ`

Text Solution

Verified by Experts

The correct Answer is:
B
`Q = int mcdT`
`= int_(20)^(4) 0.1 xx 32 xx ((T^(3))/(400^(3))) dT`
`~~ 0.002 kJ`.
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