Question

A metal of mass 1 kg at constant atmospheric pressure and at
initial temperature 20${}^{\circ }$C is given a heat of 20000 J. Find the
following :
(a) change in temperature,
(b) work done and
(c) change in internal energy.
(Given, Specific heat =$400j/kg{/}^{\circ }C.$ coefficient of cubical
expansion, $\gamma =9\times 10^{-15}{/}^{\circ }C,density\rho =9000kg/m^3,$
atmospheric pressure = $10^{5}N/m^2$

Answer 1

$(a)From\Delta Q=ms\Delta T$
$\Delta T=\frac{\Delta Q}{ms}=\frac{20000}{1\times 400}=50^{\circ }$
(b) $\Delta V=V\gamma \Delta T=\left(\frac{1}{9000}\right)(9\times 10^{-5})(50)$
$=5\times 10^{-7}{m}^3$
$\therefore W=p.\Delta V=(10^5)(65\times 10^{-7})=0.05J$
(c) $\Delta U=\Delta q-W=(2000-0.05)J$
$=19999.95J$