Building Physics 1: Thermodynamics Equations

Question 1

What is the equation for heat balance between the human body and its surroundings?

Answer 1

M – W = Q̇C + Q̇R + QE ± S, where M is metabolic rate (W), W is rate of energy expended due to external work (W), and S is rate at which heat is stored in body (W)

Question 2

What is the equation for mean radiant temperature?

Answer 2

t_r =(A1 ts1 + An tsn)/(A1+ An), where tsn is the average surface temperature of an element, and An is the corresponding surface area

Question 3

What is the equation for dry resultant temperature?

Answer 3

tres=(tr+ta)/2, where ta is air flow temperature

Question 4

What is the equation for volume flow rate?

Answer 4

V ̇=NV/3600, where V is room volume (m3) and N is number of air changes per hour (ACH)

Question 5

What is the equation for Fourier’s Law?

Question 6

What is Fourier’s Law, rearranged for steady-state?

Answer 6

Qcond/A=-((t2-t1)/(L/λ)), where Qcond/A is heat transfer rate per unit area (W/m^2)

Question 7

What is the equation for thermal resistance?

Answer 7

R=L/λ

Question 8

What is the equation for Newton’s Law of Cooling?

Answer 8

Qconv=hconv A(ts-t∞), where Qconv is heat transfer by convection (W), A is surface area (m^2), hconv is convective heat transfer coefficient (W/m2K), ts is surface temperature (K), and t∞ is the bulk temperature of fluid (K)

Question 9

What is the equation for the Stefan-Boltzmann Law for a Black Body?

Answer 9

Eb=σT^4, where Eb is the emissive power (W/m^2), T is the absolute temperature of the body (K), and σ is the Stefan-Boltzmann constant

Question 10

What is the equation for the Stefan-Boltzmann Law for a grey body?

Answer 10

E=εσT^4, where ε is the emissivity of the material (0 ≤ ε ≤ 1)

Question 11

What is the equation for emissivity?

Answer 11

ε=E/Eb

Question 12

What is the equation for radiative heat transfer?

Answer 12

Qrad=A1ε1σ(T1^4-T2^4 ), where Qrad is the heat transfer by radiation (W), A1 is the area of emitting surface (m^2), ε1 is the emissivity of the emitting surface, and T1 and T2 are the absolute temperatures of emitting (1) and receiving (2) surfaces (K)

Question 13

What is the equation for radiative heat transfer with heat transfer coefficient?

Answer 13

Qrad=hrA1(T1-T2)

Question 14

What is the equation for heat transfer coefficient?

Answer 14

h_r=f1-2(T1+T2)(T1^2+T2^2), where f1-2 is the factor which takes into account emissivity and the relative geometry of the surfaces