# Calorimetry

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Question

# Two litres of water (density = 1 g/ml) in an open lid insulated kettle is heated by an electric heater of power 1 kW. The heat is lost from the lid at the rate of 160 J/s. The time taken for heating water (specific heat capacity $4.2\mathrm{kJ}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$) from 20°C to 75°C is ___seconds.

Moderate
Solution

## Mass of 2 litres of water = 2 kg. Heat energy needed to raise the temperature of2 kg of water from 20°C to 75°C is$Q=2×\left(4.2×{10}^{3}\right)×55=4.62×{10}^{5}\mathrm{J}$If t is the time taken, heat energy supplied by the heater in time t isHeat energy lost in time t isHeat energy available for heating water isEquating $\mathrm{Q}={\mathrm{Q}}^{\mathrm{\prime }}$, we get $\mathrm{t}\simeq 550\mathrm{s}$.

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The mass, specific heat capacity and the temperature of a solid are $\frac{1}{2}$   and $80°\mathrm{C}$ respectively. The mass of the liquid and the calorimeter are  and . Initially, both are at room temperature $20°\mathrm{C}$. Both calorimeter and the solid are made of same material. In the steady state, temperature of mixture is $40°\mathrm{C}$, then find the specific heat capacity of the unknown liquid.