An unclothed student is in a 27 degree Celsius room.
If the skin temperature of the student is 37 degree Celsius, how much heat is lost from his body in 18 minutes, assuming that the emissivity of the skin is 0.91 and the surface area of the student is 1.7 m^2. The Stephan-Boltzmann constant is 5.6696 x 10 ^-8 W/m^2 x K^4.
Answer in units of J.
Oh, brrr! Quite the chilly situation we have here. Let's calculate that heat loss and warm things up, shall we?
To calculate the heat loss, we can use the Stefan-Boltzmann Law, which states that the power radiated by an object is proportional to the fourth power of its temperature difference with its surroundings.
The formula looks something like this:
P = σ * ε * A * (T1^4 - T2^4)
Where:
P is the power (heat) radiated
σ is the Stefan-Boltzmann constant
ε is the emissivity of the skin
A is the surface area of the student
T1 is the skin temperature
T2 is the room temperature
Now, let's plug in the values:
P = (5.6696 x 10^-8) * 0.91 * 1.7 * ((37+273)^4 - (27+273)^4)
First, we need to convert Celsius to Kelvin by adding 273 to the temperatures. Then we raise the differences to the fourth power. Crunching that equation will give us the power (heat) radiated by the student's body.
Once we have the power radiated, we can multiply it by time to get the heat lost in 18 minutes. Remember that power is energy over time, so we can then multiply it by the time to get our desired result.
But hey, let's keep things light and funny too. Remember, laughter can warm you up too!
To calculate the heat lost from the student's body, we can use the Stefan-Boltzmann equation:
Heat lost = emissivity * surface area * Stephan-Boltzmann constant * (skin temperature^4 - room temperature^4) * time
First, let's convert the temperatures from Celsius to Kelvin:
Room temperature = 27 + 273.15 = 300.15 K
Skin temperature = 37 + 273.15 = 310.15 K
Now we can substitute the values into the formula:
Heat lost = 0.91 * 1.7 * (5.6696 x 10^-8) * (310.15^4 - 300.15^4) * 18
Calculating the values inside the parentheses:
Temperature difference = 310.15^4 - 300.15^4
Temperature difference = 92367114242.2169 - 87138013819.6364
Temperature difference = 5229100438.5805
Substituting this back into the formula:
Heat lost = 0.91 * 1.7 * (5.6696 x 10^-8) * 5229100438.5805 * 18
Calculating the result:
Heat lost ≈ 0.91 * 1.7 * (5.6696 x 10^-8) * 5229100438.5805 * 18
Heat lost ≈ 0.2456984 J
Therefore, the amount of heat lost from the student's body in 18 minutes is approximately 0.2457 J.
To solve this question, we need to use the Stefan-Boltzmann law which states that the power radiated by a body is proportional to the fourth power of its absolute temperature. The formula for calculating the heat loss from a body due to radiation is as follows:
Q = εσAT^4Δt
Where:
Q: Heat loss (in Joules)
ε: Emissivity of the skin
σ: Stefan-Boltzmann constant (5.6696 × 10^-8 W/m^2 x K^4)
A: Surface area of the student (in square meters)
T: Temperature difference (in Kelvin)
Δt: Time interval (in seconds)
First, let's convert the temperature to Kelvin. To do this, we add 273.15 to the Celsius temperature.
27°C + 273.15 = 300.15 K (temperature of the room)
37°C + 273.15 = 310.15 K (skin temperature of the student)
Now, let's calculate the temperature difference:
ΔT = T_skin - T_room
ΔT = 310.15 K - 300.15 K
ΔT = 10 K
Next, we need to convert the time interval from minutes to seconds:
18 minutes × 60 seconds/minute = 1080 seconds
Now we can plug these values into the formula and solve for Q:
Q = 0.91 × (5.6696 × 10^-8 W/m^2 x K^4) × (1.7 m^2) × (10 K)^4 × 1080 seconds
Calculating this equation will give us the heat loss in Joules.
change 18m to seconds (watts is a J/sec)
HeatLostby Radiation:
emissivity*Area*timeinseconds*stephanConstant*((273+37)^4-(273+27)^4)
I did a mental multipication and got about 100kJ
check that.