The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 70.0 kg person of height 1.79 m would have a body surface area of approximately 1.90 m^2. What is the net amount of heat this person could radiate per second into a room at 19.0 degrees celsius if his skin's surface temperature is 31.0 degrees celsius? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.00, regardless of the amount of pigment.)
The net rate of radiative power loss is
(Area)*sigma* [T(body)^4 - T(room)^4]
The radiation is almost entirely invisible infrared.
When using the formula, T must be in Kelvin and the "sigma" is the Stefan-Boltzmann constant, which must be explained in your tesxt somewhefre. Look it up.
The negative room temperature term takes into account the radiation of the room onto the body.
I did that but the website that I do the homework on says my answer is wrong. Here are the numbers I plugged in:
(1.9 )(5.67*10^8)((31+273)^4 - (19+273)^4)
and I get the answer is 1.37*10^18 but it says that's wrong
oh, never mind, I got it, I was using the wrong value for the constant, thanks!
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2.B
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To calculate the net amount of heat that a person can radiate per second into a room, we can use the Stefan-Boltzmann law. The Stefan-Boltzmann law states that the power radiated by an object is directly proportional to the fourth power of its temperature and its surface area, and inversely proportional to its emissivity.
Let's break down the given information:
- Weight of the person (m) = 70.0 kg
- Height of the person (h) = 1.79 m
- Body surface area (A) = 1.90 m^2
- Room temperature (T_r) = 19.0 °C
- Skin surface temperature (T_s) = 31.0 °C
- Emissivity (ε) = 1.00 (for infrared radiation)
First, we need to convert the temperatures from Celsius to Kelvin, as the Stefan-Boltzmann law requires temperatures in Kelvin. To do this, we can use the formula: K = °C + 273.15.
Convert room temperature to Kelvin (T_r):
T_r = 19.0 + 273.15 = 292.15 K
Convert skin surface temperature to Kelvin (T_s):
T_s = 31.0 + 273.15 = 304.15 K
Next, we can calculate the net amount of heat radiated per second using the Stefan-Boltzmann law:
Power radiated per unit area (P/A) = σ * ε * (T_s^4 - T_r^4)
Where:
- σ (sigma) is the Stefan-Boltzmann constant: σ = 5.67 × 10^-8 W/m^2·K^4
Now, let's substitute the values into the formula:
P/A = (5.67 × 10^-8) * 1.00 * (304.15^4 - 292.15^4)
Calculate T_s^4 and T_r^4:
T_s^4 = 304.15 * 304.15 * 304.15 * 304.15
T_r^4 = 292.15 * 292.15 * 292.15 * 292.15
Substitute the values:
P/A = (5.67 × 10^-8) * 1.00 * (T_s^4 - T_r^4)
Now, multiply the power per unit area by the body surface area to find the net amount of heat radiated per second:
Net heat radiated per second = P/A * A
= P
Substitute A = 1.90 m^2:
Net heat radiated per second = (5.67 × 10^-8) * 1.00 * (T_s^4 - T_r^4) * 1.90
Perform the calculations to get the final answer.