(a) Explain specific latent heat (b)(i) Describe how the specific latent heat of fusion of ice can be determined by the method of mixtures. (ii) State two p...

Answer Details

(a) Specific latent heat. The specific latent heat of a substance is the quantity of heat required to change the state of unit mass (1 kg or 1 g) of the substance, at constant temperature, without any change in its temperature (fusion = solid to liquid; vaporization = liquid to vapour).

(b)(i) Determination of specific latent heat of fusion of ice by method of mixtures. Pour a known mass \( m_w \) of warm water at a measured temperature \( \theta_1 \) into a calorimeter of known mass and specific heat capacity. Take small pieces of dry, melting ice at \( 0^\circ\text{C} \), add them to the water and stir until all the ice just melts. Measure the final steady temperature \( \theta_2 \) and, by re-weighing, find the mass \( m_i \) of ice added. Then, heat lost by the warm water and calorimeter equals heat used to melt the ice plus heat used to warm the melted ice from \( 0^\circ\text{C} \) to \( \theta_2 \):

\[ (m_w c_w + m_c c_c)(\theta_1 - \theta_2) = m_i L + m_i c_w (\theta_2 - 0). \]

From this equation the specific latent heat of fusion of ice, L, is calculated.

(ii) Precautions:

• Dry the ice with blotting paper before adding it, to remove surface water.
• Lag (insulate) the calorimeter and stir gently, to reduce heat exchange with the surroundings.

(c) Calculation. Heat needed to melt the 20 g of ice: \[ Q = m_i L_{ice} = 20 \times 340 = 6800\,\text{J}. \]

Let the mass of steam that condenses be x grams. The steam condenses at \( 100^\circ\text{C} \) and the resulting water cools to \( 0^\circ\text{C} \), supplying the heat that melts the ice: \[ x\,L_{steam} + x\,c_w(100 - 0) = 6800 \] \[ x(2300) + x(4.2)(100) = 6800 \] \[ x(2300 + 420) = 6800 \Rightarrow x = \dfrac{6800}{2720} = 2.5\,\text{g}. \]

Total mass of water in the container = original water + melted ice + condensed steam: \[ 100 + 20 + 2.5 = 122.5\,\text{g}. \]