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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 17: Temperature and HeatProblem 10
Chapter 17, Problem 10

A constant-volume gas thermometer registers an absolute pressure corresponding to 325325 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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Understand the concept of a constant-volume gas thermometer: It measures temperature by the pressure of a gas at constant volume. The pressure is directly proportional to the temperature in Kelvin.
Recall the triple point of water: It is the temperature and pressure at which water can coexist in solid, liquid, and gas phases. The triple point temperature is 273.16 K.
Use the ideal gas law relation for constant volume: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), where \( P_1 \) and \( T_1 \) are the pressure and temperature at the triple point, and \( P_2 \) and \( T_2 \) are the pressure and temperature at the boiling point.
Identify the normal boiling point of water: The temperature at which water boils under standard atmospheric pressure is 100°C, which is 373.15 K in Kelvin.
Substitute the known values into the equation: \( P_1 = 325 \) mmHg, \( T_1 = 273.16 \) K, and \( T_2 = 373.15 \) K. Solve for \( P_2 \) using \( P_2 = P_1 \times \frac{T_2}{T_1} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Triple Point of Water

The triple point of water is the unique temperature and pressure at which water can coexist in equilibrium in its solid, liquid, and gaseous states. It is precisely defined as 0.01°C and 611.657 pascals. Understanding this concept is crucial because it provides a reference point for calibrating thermometers, including constant-volume gas thermometers.
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Constant-Volume Gas Thermometer

A constant-volume gas thermometer measures temperature by observing the pressure of a gas at a fixed volume. The pressure changes proportionally with temperature, following the ideal gas law. This type of thermometer is highly accurate and is often used to define temperature scales, making it essential for understanding how pressure readings relate to temperature changes.
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Normal Boiling Point of Water

The normal boiling point of water is the temperature at which water transitions from liquid to gas at standard atmospheric pressure (1 atm or 101325 pascals). It is 100°C. Knowing this point is important for determining the pressure reading of a constant-volume gas thermometer when it is in contact with boiling water, as the pressure will reflect the increased temperature compared to the triple point.
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Related Practice
Textbook Question

A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -20.0°C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 1.20 kg of ice and 0.80 kg of liquid water. What was the initial temperature of the piece of copper?

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Textbook Question

Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other

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Textbook Question

A steel tank is completely filled with 1.90 m3 of ethanol when both the tank and the ethanol are at 32.0°C. When the tank and its contents have cooled to 18.0°C, what additional volume of ethanol can be put into the tank?

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Textbook Question

The pressure of a gas at the triple point of water is 1.351.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?

Textbook Question

Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.

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Textbook Question

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of -15°C. How much more interior space does the dome have in the summer, when the temperature is 35°C?

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