Final answer:
The body needs to supply heat to warm the inhaled air from 0°C to 37°C, which can be calculated using the specific heat capacity of air, the ideal gas law, and the change in temperature. By finding the mass of the inhaled air and applying the formula Q = mCPΔT, we can determine the energy required for heat transfer.
Step-by-step explanation:
To calculate the amount of heat that the body must supply to warm the inhaled air from 0°C to 37°C, we can use the specific heat capacity of air along with the fact that the pressure in the lungs is held constant at 1.0 atm, making the process an isobaric one. Assuming the specific heat capacity of air remains constant during the heating, and given that air approximates an ideal gas under these conditions, we get:
Q = mCPΔT
where Q is the heat added, m is the mass of the air, CP is the specific heat capacity at constant pressure, and ΔT is the change in temperature.
First, we need to calculate the mass of the 4.0 L of air. Using the ideal gas law at Standard Temperature and Pressure (STP), we have:
PV = nRT
Where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin. At STP, 1 mole of an ideal gas occupies 22.4 L.
With 4.0 L of air inhaled, n = number of moles = (1.0 atm)(4.0 L) / (R)(273.15 K)
Next we find the mass of this air by multiplying by the molar mass of air (approximately 28.97 g/mol).
To find Q, we use the specific heat capacity of air at constant pressure, which is approximately 1.01 J/g·°C.
Finally, we have:
ΔT = 37°C - 0°C = 37°C
Q = m(1.01 J/g·°C)(37°C)
By plugging in the values for m and ΔT, we can calculate Q to find out how much heat transfer is required to warm the air to body temperature.