(A)
Interpretation:
The pressure of the air at
Concept Introduction:
Write the
Here, initial and final volume is
(A)
Explanation of Solution
Given information:
Initial Temperature is
Final Temperature is
Pressure of the air is
Convert the unit of initial temperature from degree Fahrenheit to Kelvin.
Here, temperature in Kelvin is
Substitute
Here, initial temperature is
Convert the unit of initial temperature from degree Fahrenheit to Kelvin.
Substitute
Here, final temperature is
Write the ideal gas law for states 1 and 2.
The volume is constant for an isochoric system. For a closed system, number of moles must be constant.
The Equation (3) is reduces as follows.
Substitute
Thus, the final pressure is
(B)
Interpretation:
The pressure of the air at
(B)
Explanation of Solution
Given information:
Initial Temperature is
Final Temperature is
Convert the unit of initial temperature from degree Fahrenheit to Kelvin.
Substitute
Convert the unit of initial temperature from degree Fahrenheit to Kelvin.
Substitute
Substitute
Thus, the final pressure is
(C)
Interpretation:
The volume of air that the lungs must hold when fully expanded.
Concept Introduction:
Write the expression to obtain the minimum number of moles
Here, gas constant is
Write the expression to obtain the maximum volume at maximum temperature.
Here, maximum temperature is
Write the expression to obtain the volume of air must the lungs hold when fully expanded.
Here, volume of air must the lungs hold when fully expanded is
(C)
Explanation of Solution
Since the system is closed, the number of moles is constant and can be found from minimum volume. The minimum volume occurs at the minimum temperature.
Write the expression to obtain the minimum number of moles
Substitute
Write the expression to obtain the maximum volume at maximum temperature.
Substitute
Write the expression to obtain the volume of air must the lungs hold when fully expanded.
Substitute
Thus, the volume of air must the lungs hold when fully expanded is
(D)
Interpretation:
The change in internal energy that the air undergoes.
Concept Introduction:
Write the expression to obtain the change in specific internal energy
Here, constant volume heat capacity is
Write the expression to obtain the constant pressure heat capacity of nitrogen for ideal gas
Here, gas constant is
Write the expression to obtain the constant pressure heat capacity of oxygen for ideal gas
Write the expression to obtain the parameter
Write the expression to obtain the change in internal energy
(D)
Explanation of Solution
Since this is being modeled as an ideal gas, internal energy is depends only on temperature.
Write the expression to obtain the change in specific internal energy
As we do not have the heat capacity at constant volume for the air, use constant pressure heat capacity in Equation (10).
Rewrite Equation (10).
Here, constant pressure heat capacity of air for ideal gas is
Substitute
Here, constant pressure heat capacity of nitrogen for ideal gas is
Integrate Equation (12).
Write the expression to obtain the constant pressure heat capacity of nitrogen for ideal gas
Integrate Equation (14).
From Appendix D.1, “Ideal Gas Heat Capacity”, obtain and write the constant values of nitrogen and oxygen as in Table (1).
Name | Formula | A | ||||
Nitrogen | 3.539 | 0.007 | 0.157 | |||
oxygen | 3.630 | 0.658 |
Substitute 3.539 for A,
Write the expression to obtain the constant pressure heat capacity of oxygen for ideal gas
Integrate Equation (16).
Substitute 3.630 for A,
Write the expression to obtain the parameter
Substitute
Substitute
Substitute
Write the expression to obtain the change in internal energy
Substitute
Thus, the change in internal energy does the air undergo is
(E)
Interpretation:
The work done by the lungs on the surroundings.
Concept Introduction:
Write the expression to obtain the work done
(E)
Explanation of Solution
Write the expression to obtain the work done
Substitute
Thus, the work done by the lungs is
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