The graph in Fig. E shows a -diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because they've gotten hot.) If the temperature of the air in the lung remains a reasonable °C, what is the maximum number of moles in this person's lung during a breath?
Ch 19: The First Law of Thermodynamics
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 19, Problem 1b
Two moles of an ideal gas are heated at constant pressure from °C to °C. Calculate the work done by the gas.
Verified step by step guidance1
First, convert the initial and final temperatures from Celsius to Kelvin by adding 273.15 to each temperature. This gives you the initial temperature \( T_1 = 300.15 \text{ K} \) and the final temperature \( T_2 = 380.15 \text{ K} \).
Recall that the work done by an ideal gas at constant pressure is given by the formula \( W = P \Delta V \), where \( \Delta V \) is the change in volume. However, we can also use the relation \( W = nR\Delta T \) for an ideal gas, where \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( \Delta T \) is the change in temperature in Kelvin.
Calculate the change in temperature \( \Delta T = T_2 - T_1 \). Substitute the values to find \( \Delta T = 380.15 \text{ K} - 300.15 \text{ K} \).
Use the ideal gas constant \( R = 8.314 \text{ J/mol·K} \) and the number of moles \( n = 2 \) to calculate the work done: \( W = nR\Delta T \). Substitute the values into the equation.
Finally, simplify the expression to find the work done by the gas. Remember, the units of work will be in joules (J).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in thermodynamics, expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. It describes the relationship between these variables for an ideal gas, allowing us to predict how a gas will behave under different conditions.
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Ideal Gases and the Ideal Gas Law
Work Done by a Gas at Constant Pressure
When a gas expands or contracts at constant pressure, the work done by the gas is given by the formula W = PΔV, where W is the work done, P is the constant pressure, and ΔV is the change in volume. This concept is crucial for calculating the energy transferred as work when a gas undergoes a thermodynamic process at constant pressure.
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Temperature Conversion
In thermodynamics, temperature must be expressed in Kelvin for calculations involving the Ideal Gas Law. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature. This conversion is essential for ensuring that temperature values are compatible with the equations used in gas law calculations.
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Related Practice
Textbook Question
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Textbook Question
Two moles of an ideal gas are heated at constant pressure from °C to °C. Draw a -diagram for this process.
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Textbook Question
The graph in Fig. E shows a -diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) How many joules of net work does this person's lung do during one complete breath?
Textbook Question
Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is °C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done J of work.