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.)
amount: sigma*episilon*T^4
so considering the heat out and heat in..
Netamoun=1*1.90*sigma(273+31)^4 * ((273+19)/(273+31))^4
where sigma is the Stephan constant
I get near 780 watts net
To find the net amount of heat this person could radiate per second into a room, we can use the Stefan-Boltzmann law, which relates the power radiated by an object to its surface area and temperature. The equation is as follows:
Power (P) = emissivity (e) * Stefan-Boltzmann constant (σ) * surface area (A) * (T^4 - Tr^4)
Where:
- Power (P) is the net amount of heat radiated per second
- Emissivity (e) is the emissivity of the body
- Stefan-Boltzmann constant (σ) is approximately 5.67 x 10^-8 W(m^-2)(K^-4)
- Surface area (A) is the body surface area of the person
- T is the temperature of the person's skin surface in Kelvin (K)
- Tr is the temperature of the room in Kelvin (K)
Let's calculate the values step by step:
1. Converting temperatures to Kelvin:
- Skin surface temperature = 31.0 degrees Celsius + 273.15 (to convert to Kelvin) = 304.15 K
- Room temperature = 19.0 degrees Celsius + 273.15 (to convert to Kelvin) = 292.15 K
2. Calculating the net amount of heat radiated per second:
P = 1.00 * (5.67 x 10^-8 W(m^-2)(K^-4)) * 1.90 m^2 * ((304.15 K)^4 - (292.15 K)^4)
Using a calculator, we can simplify the equation and find the final value for P.