Question

A metal of mass $1\text{kg}$ at constant atmospheric pressure and at initial temperature ${23}^{\circ }\text{C}$ is given a heat of $10000\text{J}$. Specific heat of the metal is $500{\text{J /kg}}^{\circ }\text{C}$, coefficient of cubical expansion $\gamma =8\times {10}^{-5}{/}^{\circ }\text{C}$, density = $4000{\text{kg/m}}^3$ & atmospheric pressure $={10}^5{\text{N/m}}^2$). Choose the correct statement(s).

• A. Temperature of metal body increases by ${20}^{\circ }\text{C}$.
• B. Work done by metal against atmosphere is $0.04\text{J}$.
• C. In this problem, $\Delta U=9999.96\text{J}$.
• D. None of these

Answer 1

Answer: (A), (B), (C)

In this problem, $\Delta U=9999.96\text{J}$.

Given that, $\Delta Q=10000\text{J}$
From $\Delta Q=ms\Delta T$
$\Rightarrow \Delta T=\frac{\Delta Q}{ms}=\frac{10000}{1\times 500}={20}^{\circ }\text{C}$
Since $\frac{\delta V}{V}=\gamma \Delta T$
where $\left(\gamma \right)=$ coefficient of cubical expansion
$\delta V=\gamma \Delta TV$
$=8\times {10}^{-5}\times 20\times \frac{1}{4000}[\because \rho =\frac{m}{V}\Rightarrow V=\text{mass/density}]$
$\Rightarrow \delta V=4\times {10}^{-7}{\text{m}}^3$

$\therefore$ Work done$\left(W\right)$ by the metal $=p_0\left(\delta V\right)$
$={10}^5\times 4\times {10}^{-7}$
$=4\times {10}^{-2}=0.04\text{J}$
Change in Internal energy
$\Delta U=\Delta Q-W$
$=(10000-0.04)\text{J}$
$=9999.96\text{J}$
Options (a), (b), (c) are correct.