PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Two immersion heaters, Heater X and Heater Y, are used to heat identical 1.5 kg quantities of water from 25 °C to the boiling point. The details are:
• Heater X: 2000 W, 230 V
• Heater Y: 500 W, 230 V
The specific heat capacity of water is 4200J kg−1K−1. Ignore heat losses to the surroundings.
(i) Derive an expression for the time required to raise the temperature of the water by Δθ (in K) in terms of its mass m, specific heat capacity c and the power P of the heater.
(ii) Using your expression, calculate separately the time taken by Heater X and Heater Y to bring the water to the boiling point.
(iii) Determine the electrical energy consumed, in kWh, by each heater for one complete heating cycle described above.
(iv) At an energy tariff of Rs 7.20 per kWh, compute the cost of a single heating cycle for each heater.
(v) From the viewpoint of both time efficiency and economy, which heater is preferable? Explain quantitatively, commenting on any apparent contradiction between power rating and running cost.