A person takes in a breath of 0 degrees celsius air and holds it until it warms to 37 degrees celsius. The air has an initial volume of 0.700L and a mass of 9.00*10^-4kg. Determine

a. the work done by the air on the lungs if the pressure remains constant at atm,
b.the change in internal energy of the air,and
c.the energy added to the air by heat. Model the air as if it were the monatomic gas

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.

To solve this problem, we need to apply the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system:

ΔU = Q - W

a. To determine the work done by the air on the lungs, we need to use the formula for work done by a gas:

W = PΔV

Given that the pressure (P) remains constant and the volume changes from an initial value of 0.700L to a final value determined by the temperature change, we can calculate the work done.

b. The change in internal energy (ΔU) can be calculated using the formula:

ΔU = (3/2)nRΔT

Where n is the number of moles of the gas and R is the ideal gas constant. For a monatomic gas, like air, n is given by the mass of the gas divided by the molar mass.

c. The energy added to the air by heat (Q) can be determined by rearranging the first law of thermodynamics equation:

Q = ΔU + W

Now, let's calculate each part of the problem step by step:

a. The work done by the air on the lungs:
Since the pressure remains constant (P = 1 atm), and the change in volume (ΔV) can be calculated using the ideal gas law:

ΔV = Vf - Vi

Where Vf is the final volume determined by the temperature change and Vi is the initial volume (0.700L).

b. The change in internal energy of the air:
Calculate the number of moles (n) of the gas using the given mass and the molar mass of air.
Use the ideal gas law to find the final volume (Vf) in liters.
Calculate the change in temperature (ΔT) by subtracting the initial temperature (0 degrees celsius) from the final temperature (37 degrees celsius).
Substitute the values into the formula ΔU = (3/2)nRΔT.

c. The energy added to the air by heat:
Using the equation Q = ΔU + W, substitute the values calculated for ΔU and W into the equation.