Question

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

• A. $458{\text{J kg}}^{-1}{\text{K}}^{-1}$
• B. $1232{\text{J kg}}^{-1}{\text{K}}^{-1}$
• C. $916{\text{J kg}}^{-1}{\text{K}}^{-1}$
• D. $654{\text{J kg}}^{-1}{\text{K}}^{-1}$

Answer 1

The correct option is C $916{\text{J kg}}^{-1}{\text{K}}^{-1}$

Let specific heat of unknown metal be ${}^{\prime }{s}^{\prime }$

According to principle of calorimetry,

$\text{Heat lost}=\text{Heat gain}m\times s\Delta \theta =m_1{s}_{brass}(\Delta {\theta }_1+m_2{s}_{water}+\Delta {\theta }_2)$
$\Rightarrow 192\times s\times (100-21.5)=128\times 394\times (21.5-8.4)+240\times 4200\times (21.5-8.4)$
$\Rightarrow s=916{\text{J kg}}^{-1}{\text{K}}^{-1}$