To find the answers to these questions, we will use the ideal gas law and the First Law of Thermodynamics.
a. First, we need to calculate the work done by the air on the lungs. The work done is given by the equation:
Work = Pressure * Change in Volume
Since the pressure remains constant at atm, we can use the equation:
Work = Pressure * (Final Volume - Initial Volume)
Given:
Initial Volume (Vi) = 0.700 L
Final Volume (Vf) = ?
Pressure (P) = constant atm
To find the final volume, we can use the relationship between temperature and volume for an ideal gas:
Vf = Vi * (Tf / Ti),
where Tf is the final temperature (37 degrees Celsius + 273.15 = 310.15 K) and Ti is the initial temperature (0 degrees Celsius + 273.15 = 273.15 K).
Plugging the values into the equation:
Vf = 0.700 L * (310.15 K / 273.15 K)
Now, we can calculate the work done:
Work = Pressure * (Vf - Vi)
= constant atm * (Vf - 0.700 L)
b. The change in internal energy of the air is given by the equation:
Change in Internal Energy = (3/2) * n * R * (Tf - Ti),
where n is the number of moles of the gas, R is the ideal gas constant, and Tf and Ti are the final and initial temperatures in Kelvin.
Given:
Mass (m) = 9.00 * 10^-4 kg
Molar mass of the gas = ?
Molar mass (M) = mass / number of moles
To find the number of moles, we can use the equation:
n = Mass / Molar Mass = m / M
We also need the value of the ideal gas constant (R) for monatomic gases, which is 8.31 J/(mol·K).
Plugging in the values:
Change in Internal Energy = (3/2) * (m / M) * R * (Tf - Ti)
c. The energy added to the air by heat can be calculated using the equation:
Energy added = Change in Internal Energy + Work
Plugging in the values for Change in Internal Energy and Work, we can find the energy added.