Water is stirred by an electric mixing machine The mixing ma

Water is stirred by an electric mixing machine. The mixing machine operates at steady state and draws 15 amps of current from a 110V power supply. The mixing machine also discharges heat at a rate of 1 kW. If there is 100 kg of water that is initially at 20 degree C being mixed in a well-insulated (adiabatic tank), what is the temperature of the water after 3 hours of mixing?

Solution

As the mixer is drawing electic power and also discharging heat at a rate of 1 kW. The energy apart from the discharged heat must have been going into heating the water being stirred.

We will employ the above reasoning to determine the rise in temperature of water.

The heat supplied to the water in 3 hours would be:

H = Power x time = (15 x 110 - 1000) x 3 x 60 x 60 Joules

H = 7020 KJ

Now, this heat is used to increase the temperature of water at 20 degree celsius.

7020 = 100 x 4.187 x T

or T = 16.7662

Therefore the temperature of water after three hours of heating would be 20 + 16.7662 = 36.7662 degree celsius