The process of inhalation in the lung may be modelled (very simplistically) by the pV diagram shown below , in which the pressure drops sharply in the lungs at constant volume, followed by expansion at constant pressure, and then finished by the pressure returning to atmospheric at constant volume. Assume the temperature inside the lungs is steady 37 degrees celsius.
a)How many moles of air are added to the lungs during the inhalation process? how many grams is that?
b) how much work is dones during the entire inhalation process i-f?
To answer these questions, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
a) How many moles of air are added to the lungs during the inhalation process? How many grams is that?
In the given pV diagram, during the initial phase, the pressure drops sharply at constant volume. This means that the volume increases while the pressure decreases. We can assume that the temperature remains constant at 37 degrees Celsius.
To find the number of moles of air, we need to determine the change in the number of moles from the initial to the final pressure. Since the pressure and temperature remain constant, we can use the relationship:
P1V1 = P2V2
Where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume, respectively.
Since the initial pressure drops sharply to a lower constant pressure, we can consider the initial volume (V1) as the volume at the lower pressure. Similarly, the final volume (V2) can be considered as the volume at atmospheric pressure.
Once we have the initial and final volumes, we can calculate the number of moles of air using the ideal gas law equation:
n = PV / RT
Where n is the number of moles of air, P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.
b) How much work is done during the entire inhalation process?
The work done during the entire inhalation process can be calculated using the equation:
Work = PΔV
Where P is the constant pressure during the expansion phase, and ΔV is the change in volume from the initial to the final volume.
To find the total work done, we need to consider both the expansion phase and the return to atmospheric pressure phase. For the expansion phase, we can use the work equation mentioned above. And for the return to atmospheric pressure phase, since the volume remains constant, no work is done.
To calculate the work, we need the values of the constant pressure and the change in volume from the pV diagram.
Please provide the specific values of the initial and final pressure and volumes from the pV diagram.