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

(a) From `DeltaQ=msDeltaT`
`DeltaT=(DeltaQ)/(1xx400)=50^(@)C`
(b) `DeltaV=V_(lambda)DeltaT=((1)/(9000))(9xx10^(-5))(50)=5xx10^(-7)m^(3)`
`W=p.DeltaV=(10)^(5)(5xx10^(-7))=0.05J`
(e) `DeltaU=DeltaQ-W=(20000-0.05)J`
`=19999.95J`