Question

A block100-gof metal at a temperature of$\mathbf{20}\mathbf{°}\mathbf{C}$is placed into an insulated container with 400g of water at a temperature of$\mathbf{0}\mathbf{°}\mathbf{C}$. The temperature of the metal and water ends up at $\mathbf{2}\mathbf{°}\mathbf{C}$ . What is the specific heat of this metal, per gram? Start from the Energy Principle. The specific heat of water is 4.2 J/K/g.

Short answer

The specific heat of this metal is 1.86 J/K/g.

Step-by-step solution

Given data

Mass of the metal $m_m=100g$

Initial temperature of metal $t_m=20°C$

Mass of water$m_w=400g$

Initial temperature of water$t_w=0°C$

Final temperature$T=2°C$

Heat capacity of water $c_w=4.2J/K/g$

Definition of specific heat

Heat capacity is a physical property of matter, defined as the amount

of the heat to be supplied to an object to produce a unit change in its

temperature.

Determine the specific heat of metal

Heat lost by metal = Heat gain by water

$$\begin{gathered} m_m{c}_m\left(20°C-2°C\right)=m_w{c}_w\left(20°C-2°C\right) \\ \Rightarrow \left(100\right)c_m\left(18\right)=\left(400\right)\left(4.2\right)\left(2\right) \\ {c}_m=\frac{\left(400\right)\left(4.2\right)\left(2\right)}{\left(100\right)\left(18\right)}=1.86J/K/g \end{gathered}$$

Hence, specific heat of metal will be $c_m=1.86J/K/g$.