A person's normal body-temperature is 97 ^ ^ ^ F . Determine the rate at which heat flows out of their body through the clothes, assuming the following values: room temperature = 47 ^ ^ ^ F , surface of the body under

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 356 J s^ -1

The temperature difference in Fahrenheit is

\Delta T_{F} = 97 - 47 = 50 ^{}^{{}^{\circ}} F

Converting this temperature difference to Celsius:

\Delta T_{C} = \dfrac{5}{9} \times \Delta T_{F} = \dfrac{5}{9} \times 50 = \dfrac{250}{9} ^{}^{{}^{\circ}} C

The rate of heat flow is given by Fourier's law of heat conduction:

\dfrac{dQ}{dt} = \dfrac{KA \Delta T}{d}

Substituting the given values

K = 0.04 \text{ J s}^{-1} \text{ m}^{-1} ^{}^{{}^{\circ}} C^{-1}

,

A = 1.6 \text{ m}^2

, and

d = 0.5 \text{ cm} = 0.005 \text{ m}

:

\dfrac{dQ}{dt} = \dfrac{0.04 \times 1.6 \times \dfrac{250}{9}}{0.005}

\dfrac{dQ}{dt} = 8 \times 1.6 \times \dfrac{250}{9} = \dfrac{3200}{9} \approx 355.56 \text{ J s}^{-1}

Rounding to the nearest integer, the rate of heat flow is

356 \text{ J s}^{-1}

.

A person's normal body-temperature is 97 ^ ^ ^ F . Determine the...

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