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`)

Answer

(i) `70^(@)C` (ii) `0.05 J` (iii) `19999.95 J`

Explanation

(a) From `DeltaQ = "ms"DeltaT`
`DeltaT = (DeltaQ)/(ms) = (20000)/(1 xx 400) = 50^(@)C`
(b) `DeltaV = V_(gamma)DeltaT = ((1)/(9000)) (8xx 10^(-5))(50)`
=`5 xx 10^(-7)m^(3)`
`therefore W = PDeltaV = (10^(5)) (5 xx 10^(-7)) = 0.05J`
(c) `DeltaU = DeltaQ - W = (20000-0.05)J`
=`19999.95J`