Latent Heat of Fusion and Vaporization

Change of State

A substance can exist in three states: solid, liquid and gas. A change in state from solid to liquid on heating is called fusion or melting. When some heat is supplied to a solid, it starts melting as it attains required temperature and the temperature remains constant until whole the solid melts. This constant temperature is called melting point of the solid. In the same way, on cooling a liquid, it changes into solid as it loses the sufficient amount of heat and this is called solidification or freezing. During this solidification, the temperature remains constant which is freezing point. The freezing point is different from different liquids. In general crystalline substances have same melting and freezing point but in non-crystalline solid melting and freezing are not same. For an example: butter has melting point 30^oCand freezing point 22 ^oC.

Latent heat

Latent heat of a substance is the amount of heat required to change the state of a unit mass of the substance from solid to liquid or from liquid to vapour without changing the temperature. During heating the substance, the heat has been used up in changing the state; temperature remaining the same till the state of the entire substance has changed. This energy is used up in separating the molecules farther apart and as work must be done against the required to change the state of a substance. That is why heat energy spent in a change of state is called latent heat i.e. heat which is hidden from the thermometer. Latent heat is represented by L and is measured in Jkg^-1 or calg^-1. There are two types of latent heat i.e. latent heat of fusion and latent heat of vaporization.

Latent Heat of fusion

Latent heat of fusion is defined as the amount of heat required to change a unit mass of a substance from the solid state to liquid state at a constant temperature. The latent heat of fusion of ice is defined as the amount of heat required to change 1 g of ice from 0to water at the same temperature. For ice, its value is 3.36 10⁵ J Kg^-1 in SI-units or 80cal g^-1 in CGS-system.

Latent Heat of Vaporization

When a liquid is heated, it starts boiling and is changed into the vapour state. During the process, the temperature of the liquid remain constant and the amount of heat energy is utilized to change its' state only i.e. from a liquid state to vapour state which is called latent heat of vaporization.

Latent heat of vaporization of liquid is defined as the amount of heat required to change the unit mass of liquid at boiling point into vapour at the same temperature. So, latent heat of steam is defined as the amount of heat required to change a unit mass of water from100to steam at the same temperature. The latent heat of vaporization is 2.26 × 10⁶ Jkg^-1or 540 calg^-1.

When heat is supplied to a piece of ice of 1 g at -10^oC, the change in temperature is shown in the figure. The temperature of ice first increases from -10^oC to 0 ^oCand it melts completely when 80 calories of heat is given to it, temperature remain same as 0^oC. To convert the water into the steam, 540 cal of heat energy is supplied.

Determination of Latent Heat of Fusion of Ice by the Method of Mixture

Following are the steps to determine the latent heat of fusion of ice:

1. A calorimeter with stirrer is taken and it is weighted.
2. Some water is poured into to calorimeter then the mass and temperature of a calorimeter, stirrer and water is taken.
3. The small piece of ice is taken and the temperature noted say (0 ^oC).
4. The piece of ice is dropped into the calorimeter.
5. The mixture is stirred until all the ice is melted then the final temperature and mass of mixture is taken.

Let,

m₁= mass of calorimeter and stirrer

m₂ = mass of calorimeter, stirrer and water

m_w = m_{1 -} m₂ = mass of water only

m₃ = mass of calorimeter, stirrer, water and ice

m= m_{3 -} m₂ = mass of ice only

= temperature of water, stirrer and calorimeter

= temperature of ice, water and calorimeter

= temperature of mixture

s_c = specific heat capacity of a calorimeter

s_w = specific heat capacity of water

l_f = Latent heat of fusion = ?

Heat loss by water and calorimeter, $$= m_ws_w(\theta_1 - \theta) + m_1s_c(\theta_1 - \theta)$$

$$=(m_ws_w + m_1s_c)(\theta_1 - \theta)$$

Heat gain by ice when it changes from 0⁰ ice to 0⁰ water and 0⁰ water to θ⁰ water \( = m l_f +m_1s_w(\theta_1 -0) \)

From principle of calorimetry

\begin{align*} \text {Heat gain} &= \text{Heat loss} \\(m l_f +m_1s_w(\theta_1 -0) &= m_ws_w(\theta_1 - \theta) + m_1s_c (\theta_1 - \theta) \\m l_f &= (m_ws_w + m_1s_c)(\theta_1 - \theta)- ms_w(\theta_1 -0) \\\therefore l_f &= \frac {(m_ws_w + m_1s_c)(\theta_1 - \theta)- ms_w \theta_1 }{m} \\ \end{align*}