Question

hen resting, a person has a metabolic rate of about 7.84 x 105 joules per hour. The person is submerged neck-deep into a tub containing 2.06 x 103 kg of water at 20.9 °C. If the heat from the person goes only into the water, find the water temperature in degrees Celsius after half an hour.

Answer 1

Answer on Question #37948, Physics, Molecular Physics | Thermodynamics

Question:

When resting, a person has a metabolic rate of about $7.84 \times 10^{5}$ joules per hour. The person is submerged neck-deep into a tub containing $2.06 \times 10^{3} \mathrm{~kg}$ of water at $20.9{}^{\circ} \mathrm{C}$. If the heat from the person goes only into the water, find the water temperature in degrees Celsius after half an hour.

Answer:

$$Q = c m (T _ {2} - T _ {1})$$

where $m$ is mass, $T_{2} - T_{1}$ – change of temperature, $Q$ is amount of heat.

Therefore, final temperature equals:

$$T _ {2} = T _ {1} + \frac {Q}{c m}$$

Amount of heat equals:

$$Q = 7.84 * 10^{5} \frac{J}{h} * 0.5 \, h = 3.92 * 10^{5} J$$

Finally:

$$T _ {2} = T _ {1} + \frac {Q}{c m} = 20.9 + \frac {3.92 * 10^{5}}{4183 * 2.06 * 10^{3}} = 21.16 \, {}^\circ \mathrm{C}$$

Answer: $21.2{}^{\circ} \mathrm{C}$