Calculate the surface temperature of a human body

[Superdreamer]

I am unsure about some of my formulae and answers I would be very grateful if someone could clarify these please

Q1 The insulating layer on the inner wall of a building is made from a
compound layer of laminated board (inner) and styrofoam (outer). The
thickness of the board is 0.02 m and of the styrofoam, 0.06 m. If the
temperature at the surfaces of the layer are 20C (inner) and 5C (outer),
calculate the rate of flow of heat per m 2 through the layer and the
temperature at the board-styrofoam interface. The thermal conductivities
are 0.1 Js -1 m -1 C -1 for the board and 0.01 J s -1 m -1 C -1 for the styrofoam.

used the formula R=L/k to find the resistance of both then subbed in formula P=A(T2-T1)/(R1+R2)
Answer 2.42W

Q2 Calculate the surface temperature of a human body of surface area 1.2
m 2 , which emits radiation at a rate of 597 W. Assume that the body
behaves as a perfect black body. If the temperature of the surroundings is
18° °° °C, calculate the net loss of heat by radiation by the body.

Used the formula Aε(5.6703x10^-8)T^4=Q/T=P

Answer T=306.10k
Orig temp T=291.16k
Aε(5.67...)(T2^4-T1^4)
Answer 108.31W

Q3 Calculate the root mean square speed of nitrogen
molecules at 20 C. At what temperatures will the RMS speed be a) half that
value and b) twice that value?
The molar mass of nitrogen is 28x10 -3 kg mol -1 .

Vrms=sq root 3RT/M
Answer 510.89
Answer 2 73.28k
Answer 3 1,172.60k

Please confirm if these are done correctly or if not please lead me in the right direction thanks!

 

[Astronuc]

Try these references:

Heat transfer by conduction
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c2

Heat transfer by radiation (Stefan-Boltzmann Law)
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2

Answers to C are correct (Maxwell-Boltzmann distribution)
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4

One can use the calculators to self-check for b and c.

 

[quicknote]

A1 To calculate the rate of flow of heat per square meter, we can use the formula Q/t = kA(T2-T1)/d, where Q is the rate of heat flow, k is the thermal conductivity, A is the area, T2 and T1 are the temperatures at the two surfaces, and d is the thickness of the material.

First, we need to calculate the resistance of each layer using the formula R = d/k. For the board, R = 0.02/0.1 = 0.2 m^2 C/W. For the styrofoam, R = 0.06/0.01 = 6 m^2 C/W.

Then, we can use the formula P = A(T2-T1)/(R1+R2) to calculate the rate of heat flow. Plugging in the values, we get P = (1m^2)(20-5)/(0.2+6) = 2.42 W.

To find the temperature at the board-styrofoam interface, we can use the formula T1 + P(R1/R1+R2) = T2 - P(R2/R1+R2). Plugging in the values, we get T1 + (2.42)(0.2/0.2+6) = 5, so T1 = 4.99°C.

A2 To calculate the surface temperature of a human body, we can use the Stefan-Boltzmann law: P = AεσT^4, where P is the rate of heat emission, A is the surface area, ε is the emissivity (assumed to be 1 for a perfect black body), σ is the Stefan-Boltzmann constant, and T is the temperature.

Plugging in the values, we get 597 = (1.2m^2)(5.6703x10^-8)(T^4), so T = 306.10 K. This is the temperature at which the body will emit 597 W of heat.

To calculate the net loss of heat by radiation, we can use the formula Q = Aεσ(T^4-Tsur^4), where Q is the net loss of heat, A is the surface area, ε is the emissivity, σ is the Stefan-Boltzmann constant, and Tsur is the temperature of the surroundings.

Plugging in the