A person takes about 20 breaths per minute with 0.5 litre of air in each breath. How much heat is removed per hour by the moisture in the exhaled breath if the incoming air is dry and the exhaled breath is fully saturated? Assume that the water vapour pressure in the saturated exhaled air is 24 torr.

That's 10 liters of air per minute. If the partial pressure of exhaled H2O is 24 torr, the number of moles of water (at 20 C and 1 atm) is

(10/24)*24/760 = 1.32*10^-2 moles
which has a mass of 0.237 g. Multiply that by 60 for the mass loss per hour. It's about 14.2 g.

For heat removal, multiply that by the heat of vaporization of H2O

To calculate the amount of heat removed per hour by the moisture in the exhaled breath, we need to use the concept of heat of vaporization and the Ideal Gas Law.

1. First, let's find out the amount of water vapor in the exhaled breath per minute.
- To do this, we need to calculate the amount of water vapor in one breath, considering that it is fully saturated.
- The vapor pressure of water at 37°C (body temperature) is approximately 47 torr (from tables).
- The difference in vapor pressures between the exhaled and inhaled breath is: 47 - 24 = 23 torr, which represents the pressure increase due to water vapor inhaled.

2. Convert 23 torr to atm:
- 1 atm = 760 torr
- 23 torr / 760 torr = 0.030 atm

3. Use the Ideal Gas Law to calculate the amount of water vapor in one breath:
- The Ideal Gas Law equation is PV = nRT (where P = pressure, V = volume, n = amount of substance, R = gas constant, and T = temperature)
- We know that the pressure (P) for water vapor in one breath is 0.030 atm, the volume (V) is 0.5 liters, and the temperature (T) is 37°C (310.15 K).
- Rearranging the equation to solve for n, we get n = PV / RT.

n = (0.030 atm * 0.5 L) / (0.0821 L.atm/(mol.K) * 310.15 K)

- n = 0.000938 mol of water vapor in one breath

4. Calculate the amount of water vapor per minute:
- Since we take about 20 breaths per minute, multiply the amount of water vapor per breath by the number of breaths per minute:

0.000938 mol/breath * 20 breaths/minute = 0.01876 mol/minute

5. Calculate the amount of water vapor per hour:
- Since there are 60 minutes in an hour, multiply the amount of water vapor per minute by 60:

0.01876 mol/minute * 60 minutes/hour = 1.126 mol/hour

6. Finally, calculate the heat removed per hour:
- The heat of vaporization for water is approximately 40.79 kJ/mol.
- Multiply the amount of water vapor per hour by the heat of vaporization:

1.126 mol/hour * 40.79 kJ/mol = 45.99 kJ/hour

Therefore, approximately 45.99 kJ of heat is removed per hour by the moisture in the exhaled breath.

To calculate the amount of heat removed per hour by the moisture in the exhaled breath, we need to determine the amount of water vapor in the exhaled breath and the corresponding heat of vaporization.

Step 1: Calculate the amount of water vapor in each breath
The water vapor pressure in the saturated exhaled air is given as 24 torr. We can convert this to an equivalent pressure in Pascals using the conversion factor: 1 torr = 133.3224 Pascals.

P = 24 torr * 133.3224 Pa/torr = 3199.73 Pa

To calculate the amount of water vapor (in moles) in each breath, we need to use the ideal gas law:

PV = nRT

Where:
P is pressure (in Pascals)
V is volume (in liters)
n is the number of moles
R is the ideal gas constant (8.314 J/mol·K)
T is the temperature (in Kelvins)

In this case, we know the pressure (P), volume (V = 0.5 liters), and temperature (T), and we need to solve for n.

Step 2: Calculate the number of moles of water vapor in each breath
Rearranging the ideal gas law equation, we have:

n = PV / RT

Substituting the known values:

n = 3199.73 Pa * 0.5 L / (8.314 J/(mol·K) * T)

We need to know the temperature in Kelvins to proceed. Let's assume a standard body temperature of 37 degrees Celsius.

T = 37 degrees Celsius + 273.15 = 310.15 K

n = 3199.73 Pa * 0.5 L / (8.314 J/(mol·K) * 310.15 K)

Calculate the value of n.

Step 3: Calculate the heat removed per hour
To calculate the heat removed per hour, we need to determine the heat of vaporization, which is the amount of heat required to convert one mole of liquid into vapor at constant temperature and pressure.

The heat of vaporization for water is approximately 40.7 kJ/mol.

Finally, we can calculate the heat removed per hour:

Heat removed per hour = (heat of vaporization) * (number of moles of water vapor per breath) * (number of breaths per minute) * (60 minutes per hour)

Substitute the values we obtained earlier and complete the calculation to find the answer.