Question

An unknown metal of mass $192g$ heated to a temperature of $100^{\circ }C$ was immersed into a brass calorimeter of mass $128g$ containing $240g$ of water at a temperature of $8.4^{\circ }C$. Calculate the specific heat (in $Jk{g}^{-1}{K}^{-1})$ of the unknown metal if water temperature stablizes at $21.5^{\circ }C$. (Specific heat of brass is $394Jk{g}^{-1}{K}^{-1})$

Answer 1

Answer: 916

Let specific heat of unknown metal be ‘$s$’ According to principle of calorimetry, Heat lost
= Heat gain $m\times S\Delta \theta =m_1{S}_{\text{brass}}(\Delta {\theta }_1+m_2{S}_{\text{water}}+\Delta {\theta }_2)$
$\Rightarrow 192\times S\times (100-21.5)$
$=128\times 394\times (21.5-8.4)$
Solving we get, $+240\times 4200\times (21.5-8.4)$
$S=916Jk{g}^{-1}{k}^{-1}$