Question

Five grams of water initially at ${{20}^{0}}C$ is frozen into ice at ${{0}^{0}}C$. The specific heat capacity of water, $C=4200Jk{{g}^{-1}}$ and the specific latent heat of fusion of ice, $L=336J{{g}^{-1}}$. Calculate the amount of heat evolved.

Answer 1

We need to understand the different phases or the stages in which the energy conversions take place when a specific amount of water in liquid state is converted to ice, i.e., to solid state in order to find the energy involved in this problem as the solution.

Complete Solution Step-by-Step:
We know that any matter can exist in different states depending on its environmental conditions and the intrinsic property of the matter. The water remains liquid at room temperature and has a tendency to get solidified when the temperature drops below zero degree centigrade. This conversion from liquid to solid involves a lot of energy release as the solid state is a low energy state of any matter.

In this case, 5g of water in liquid state at ${{20}^{0}}C$ is cooled to ${{0}^{0}}C$. This cooling results in the energy release in the form of heat from the molecules, thus resulting in the ice. The two steps involved in a phase transition are – the energy change due to the change in temperature of the surrounding, here from ${{20}^{0}}C$ to ${{0}^{0}}C$ and the heat involved in hidden form (latent heat) which results in phase transition.

We have the relation which can be used to find the heat evolved in our process. The heat evolved as the temperature drops is given as –

& {{Q}_{1}}=mC\Delta T \\\ & \Rightarrow {{Q}_{1}}=(5\times {{10}^{-3}}kg)(4200Jk{{g}^{-1}})({{20}^{0}}C-{{0}^{0}}C) \\\ & \therefore {{Q}_{1}}=420J \\\ \end{aligned}$$ The heat evolved at the time of phase transition is – $$\begin{aligned} & {{Q}_{2}}=mL \\\ & \Rightarrow {{Q}_{2}}=(5g)(336J{{g}^{-1}}) \\\ & \therefore {{Q}_{2}}=1680J \\\ \end{aligned}$$ So, the total heat evolved is given as – $$\begin{aligned} & Q={{Q}_{1}}+{{Q}_{2}} \\\ & \Rightarrow Q=420J+1680J \\\ & \therefore Q=2100J \\\ \end{aligned}$$ This is the required solution. **Note:** The heat involved in the phase transition doesn’t show any variation in temperature of the system and therefore is called the latent heat. The latent heat is involved in melting or fusion and in evaporation which is the hidden energy of the system.