Hey
I'm lost on this physics problem can anyone tell me which equations i'm suppose to use in these questions
a) A skier inhales a breath of air at Temp-air = 3.9 ¢XC and exhales it as Volume-air = 1.92 liters of air at Temp-body = 37 ¢XC and atmospheric pressure of P = 95.9 kPa, evaporating mass = 24.8 mg of water from the lungs and breathing passages with each breath. At body temperature the latent heat of vaporization of water is Lv = 2255 x 103 J kg−1. Given that air has a density of £l = 1.13 kg m−3 and a heat capacity of c = 1.02 kJ kg-1 K−1 under the relatively constant pressure conditions of breathing:
(i) What is the magnitude of heat lost in each breath from the evaporation process?
(ii)What is the magnitude of heat lost in each breath from just warming the air?
(iii) If the skier is breathing at the moderate rate of 18.0 per minute, what is the magnitude of the rate of heat loss from both of these modes?
(b) The skier's boyfriend, who has a surface area of 1.4 m2, is wearing a down jacket and trousers of thickness 2.5 cm and thermal conductivity of £e = 0.0207 W m−1 K−1. If his skin temperature is at a comfortable 34.2 ¢XC and the outside of his costume is at the same temperature as the ski-field air:
(i) What is the magnitude of the rate of heat loss by conduction at this ski-field temperature?
(ii) What is the lowest ski-field temperature for which the costume is adequate (i.e. comfortable) if it is possible to safely lose 58.6 W by conduction alone?
Cheers
To solve these physics problems, you need to use various equations related to heat transfer and thermodynamics. I will walk you through the process of solving each question.
a)
(i) To find the magnitude of heat lost in each breath from the evaporation process, you need to use the equation for heat transfer by evaporation:
Q = m * Lv
Where Q is the heat transferred, m is the mass of water evaporated, and Lv is the latent heat of vaporization of water.
Substituting the given values:
Q = (24.8 mg) * (2255 x 10^3 J kg^(-1))
(ii) To find the magnitude of heat lost in each breath from just warming the air, you can use the specific heat equation:
Q = mcΔT
Where Q is the heat transferred, m is the mass of air, c is the specific heat capacity of air, and ΔT is the change in temperature.
Substituting the given values:
Q = (1.92 liters) * (1.13 kg m^(-3)) * (1.02 x 10^3 J kg^(-1) K^(-1)) * (37 ¢XC - 3.9 ¢XC)
(iii) To find the magnitude of the rate of heat loss from both evaporation and warming of the air, you need to consider the breathing rate. The rate of heat loss can be calculated by multiplying the heat lost in each breath by the breathing rate.
(b)
(i) To find the magnitude of the rate of heat loss by conduction, you need to use the equation:
Q = k * A * ΔT / d
Where Q is the rate of heat transfer, k is the thermal conductivity, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.
Substituting the given values:
Q = (0.0207 W m^(-1) K^(-1)) * (1.4 m^2) * (34.2 ¢XC - T_ski-field)
(ii) To find the lowest ski-field temperature for which the costume is adequate, you need to rearrange the equation for conduction rate and solve for ΔT. Once you have ΔT, you can add it to the comfortable skin temperature of 34.2 ¢XC to find the lowest ski-field temperature.
Q = k * A * ΔT / d
Solving for ΔT:
ΔT = (Q * d) / (k * A)
Substituting the given values and rearranging the equation will give you the desired value.
These are the main equations you need to use to solve the given physics problems. Make sure to substitute the correct values and units to get the correct numerical answers.