Question

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.

Answer 1

Answer:

The temperature after half an hour is $19.3002^{\circ}$

Solution:

As per the question;

Metabolic rate of the person is 3.0105 J/h

Temperature, T = $19.30^{\circ}$

Mass of the water, $m_{w} = 1.2103 kg$

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

Now,

Heat, $Q = ms\Delta t$

Thus heat transfer in half an hour:

$Q = 3.0105\times 0.5 = 1.505 J$

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

$Q = m_{w}s\Delta T = ms(T' - T)$

where

s = 4186 J

$1.505 = 1.21103\times 4186\times (T' - 19.30^{\circ})$

$T' = 19.3002 ^{\circ}$