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Heat energy of 10,000 J is supplied to a...

Heat energy of 10,000 J is supplied to a metal block of mass 600 g at atmospheric pressure. The initial temperature of the block is `20^@C`, specific heat of metal `= 300 J kg^(-1) C^(-1) ` , relative density of metal = 7.0, coefficient of volume expansion of metal `= 6 xx 10^(-5) ""^@C^(-1)` and atmospheric pressure, `P = 10^5` Pa. Also, Heat energy supplied = mass x specific heat x change in temperature
The amount of work done by the block on the surroundings where `Delta W = P Delta V` is

A

0.042 J

B

0.051 J

C

0.063 J

D

0.074 J

Text Solution

Verified by Experts

The correct Answer is:
B
Given , density of metal `rho = 7 xx 1000 kg m^(-3)`
` = 7000 kg m^(-3)`
Volume of the block is
` V=m/rho = (0.6 kg)/(7000 kg//m^(-3)) = 6/7 xx 10^(-4) m^3`
`therefore ` Increase in volume ` Delta V = gammaV Delta T`
` = 6 xx 10^(-5) xx 6/7 xx 10^(-4) xx 100`
` = 36/7 xx 10^(-7) m^3`
Work done , `Delta W = P Delta V = 10^5 xx 36/7 xx 10^(-7) `
= 0.051 J
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