When resting, a person has a metabolic rate of about 3.0 105 joules per hour. the person is submerged neck-deep into a tub containing 1.21 103 kg of water at 19.30° c. if the heat from the person goes only into the water, find the water temperature after half an hour.

The temperature after half an hour is

Solution:

As per the question;

Metabolic rate of the person is 3.0105 J/h

Temperature, T =

Mass of the water,

Time duration, t = 0.5 h = 30 min = 180 s

Now,

Heat,

Thus heat transfer in half an hour:

Now, the temperature of water after half an hour, T' is given by:

where

s = 4186 J

need to see circuit to get time constant