A metal of mass 1 kg at constant atmospheric pressure and at initial temperature `20^@C` is given a heat of 20000J. Find the following
(a) change in temperature,
(b) work done and
(c) change in internal energy.
(Given, specific heat `=400J//kg-^@C`, cofficient of cubical expansion, `gamma=9xx10^-5//^@C`, density `rho=9000kg//m^3`, atmospheric pressure `=10^5N//m^2`)

Explanation

Here, `m=1 kg, T= 20.^(@)C`,
`dQ= 20000J, DeltaT=?`
From `dQ=cmdT, dT=(dQ)/(cm)= (20000)/(400xx1)= 50.^(@)C`
Volume, `V=m/(rho)= 1/(9000)m^(3)`
Change in volume, `dV= gamma V DeltaT`
`=9xx10^(-5)xx1/(90000)xx50= 5xx10^(-7)m^(3)`
Work done, `W=PdV= 10^(5)xx5xx10^(-7)= 0.05J`
According to first law of thermodynamics,
`dU=dQ-dW= 20000-0.05= 19999.95J`