Textbook Question
Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other
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Ch 17: Temperature and Heat
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 17, Problem 7
The pressure of a gas at the triple point of water is atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?
Verified step by step guidance1
Identify the initial conditions: The pressure of the gas is 1.35 atm, and the volume remains unchanged. This suggests that we are dealing with a scenario where the volume is constant, which is a key aspect of the problem.
Recognize the relationship between pressure and temperature for a gas at constant volume. According to Gay-Lussac's Law, the pressure of a gas is directly proportional to its temperature when the volume is held constant. This can be expressed as: , where P is pressure and T is temperature.
Determine the temperature at which CO2 solidifies. Carbon dioxide solidifies at a temperature of approximately -78.5°C, which is equivalent to 194.65 K. This is the temperature at which you need to calculate the new pressure.
Use the proportional relationship from Gay-Lussac's Law to set up the equation: . Here, is the initial pressure (1.35 atm), is the initial temperature (273.15 K, the triple point of water), is the final pressure, and is the final temperature (194.65 K).
Solve for the final pressure using the equation: . Substitute the known values to find the pressure at the temperature at which CO2 solidifies.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triple Point
The triple point of a substance is the unique temperature and pressure at which the three phases (gas, liquid, and solid) coexist in equilibrium. For water, this occurs at 0.01°C and 611.657 pascals. Understanding the triple point is crucial for determining phase changes and conditions under which substances transition between states.
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Phase Diagrams
Ideal Gas Law
The Ideal Gas Law, expressed as PV=nRT, relates the pressure (P), volume (V), and temperature (T) of a gas with its amount in moles (n) and the ideal gas constant (R). It is essential for predicting how changes in temperature affect pressure when volume is constant, assuming the gas behaves ideally.
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Phase Transition of CO2
CO2 solidifies at a specific temperature and pressure, known as its sublimation point, which is -78.5°C at 1 atm. Understanding this phase transition is crucial for determining the conditions under which CO2 changes from gas to solid, affecting its pressure if the volume remains constant.
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Related Practice
Textbook Question
One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?
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Textbook Question
Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0°R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point temperature of water on the Rankine scale?
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Textbook Question
Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.
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Textbook Question
A constant-volume gas thermometer registers an absolute pressure corresponding to mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?
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