Answer to Question #90438 in Mechanics | Relativity for AWESOME

Question

Water of mass 1002kg is poured in a calorimeter heated with an electric heater rated 1000w. if the initial temperature of water is 25 o C, calculate the time it will take to raise the temperature to 75oC. (neglect the specific heat capacity of calorimeter and take the specific heat capacity of water to be 4200jkg-1k-1

Answer 1

During the heating, the water temperature should be changed to

$$\Delta T = 75-25 = 50 °K.$$

There is a need to waste 4200 joules of energy to increase the temperature of 1 liter (or kilogram) of water for 1 °K. For the total water mass m = 1002 kg and the difference between the initial and final temperatures 50 °K, the required energy is 

$$U = \Delta T*Q*m = 50*4200*1002 = 210420000 j.$$

The electric heater rated P = 1000 W can produce that amount of energy for the time

$$t = \frac{U}{P} = \frac {210420000}{1000} = 210420 s = 58.45 h.$$