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 =$400 j/kg/^{\circ}C.$ coefficient of cubical
expansion, $\gamma =9 \times 10^{-15} /^{\circ}C, \, density \, \, \rho =9000 kg/m^3,$
atmospheric pressure = $10^5N/m^2$

Answer 1

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