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A gas thermometer registers an absolute pressure corresponding to 325 \(\mathrm{mm}\) 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?

Short Answer

Expert verified
The pressure reading at the boiling point is approximately 444.7 mm Hg.

Step by step solution

01

Understand the Triple Point and Boiling Point

The triple point of water is a condition where water exists simultaneously in solid, liquid, and gaseous states. It occurs at a temperature of 273.16 K and a specific pressure. The normal boiling point of water is at 100°C or 373.15 K, under standard atmospheric pressure.
02

Use the Ideal Gas Law Relationship

Assuming the gas thermometer behaves like an ideal gas, the relation between pressure (P) and temperature (T) can be expressed as follows: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), where \( P_1 \) is the initial pressure at the triple point and \( T_1 \) is the triple point temperature, and \( P_2 \) and \( T_2 \) are the corresponding values at the boiling point.
03

Substitute Known Values

Given that \( P_1 = 325 \) mm Hg at \( T_1 = 273.16 \) K and that \( T_2 = 373.15 \) K at the boiling point. Thus, \( \frac{325}{273.16} = \frac{P_2}{373.15} \).
04

Solve for \( P_2 \)

Rearrange the equation to solve for \( P_2 \): \( P_2 = \frac{325 \times 373.15}{273.16} \). Calculate this to find \( P_2 \).
05

Perform the Calculation

Perform the calculation: \( P_2 = \frac{325 \times 373.15}{273.16} \approx 444.7 \) mm Hg. Therefore, the pressure reading at the boiling point is approximately 444.7 mm of mercury.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It explains how energy is transferred in the form of heat, leading to various state changes in a system. There are four laws in thermodynamics that define and govern these processes.
This field is crucial when studying gases under different conditions. For gases, the ideal gas law is a pivotal equation: it relates pressure, volume, temperature, and the number of moles of a gas. In this context, we are particularly interested in how gas pressure changes with temperature, guided by this law.
  • The first law encompasses the principle of energy conservation.
  • The second law introduces the concept of entropy.
  • The third law states that absolute zero temperature is unattainable.
  • The zeroth law defines temperature equilibrium among systems.
Each law helps us understand how substances behave from an energetic perspective.
Triple Point
The triple point of a substance is a thermodynamic concept where all three states of matter—solid, liquid, and gas—can coexist in equilibrium. For water, this unique condition occurs at exactly 273.16 Kelvin and a minute pressure of 611.657 pascals. This specific point is useful in precision temperature measurements.
It serves as a fixed reference for thermometers, like in the given gas thermometer exercise.
  • Serves as an official temperature point for the thermodynamic temperature scale.
  • Helps in recalibrating and verifying temperature measurements across different laboratory conditions.
  • Is crucial for scientific experiments needing precise control of phase conditions.
Understanding the triple point is essential for grasping the full scope of temperature-dependent experiments.
Boiling Point
The boiling point of a substance is the temperature at which its vapor pressure equals the surrounding pressure, causing it to change from liquid to gas. For water, under normal atmospheric pressure, this occurs at 100°C or 373.15 Kelvin.
Boiling is a critical concept because it signifies a physical change from one state to another, driven by energy input.
  • Identifies the temperature needed for phase transitions in liquids.
  • Is affected by atmospheric conditions: higher altitudes have lower boiling points.
  • Plays a role in culinary, industrial, and scientific applications requiring precise temperature and pressure conditions.
Recognizing how the boiling point changes under different pressures aids in experiments including those involving the ideal gas law.
Absolute Pressure
Absolute pressure measures the pressure relative to a perfect vacuum. Unlike gauge pressure, which is measured relative to atmospheric pressure, absolute pressure provides the true measure. It is particularly important in scientific and engineering calculations where exact pressure readings are needed.
In this scenario with the gas thermometer, we use absolute pressure to ensure the readings are unaffected by local atmospheric conditions.
  • Calculated as the sum of gauge pressure and atmospheric pressure.
  • Used in contexts where precise calibration and measurement are necessary.
  • Essential for calculations in thermodynamics and fluid dynamics.
In experiments utilizing the ideal gas law, understanding absolute pressure against gauge pressure ensures accurate results.

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Most popular questions from this chapter

A copper calorimeter can with mass 0.446 \(\mathrm{kg}\) contains 0.0950 \(\mathrm{kg}\) of ice. The system is initially at \(0.0^{\circ} \mathrm{C} .\) (a) If 0.0350 \(\mathrm{kg}\) of steam at \(100.0^{\circ} \mathrm{C}\) and 1.00 atm pressure is added to the can, what is the final temperature of the calorimeter can and its contents? (b) At the final temperature, how many kilograms are there of ice, how many of liquid water, and how many of steam?

In a container of negligible mass, 0.200 \(\mathrm{kg}\) of ice at an initial temperature of \(-40.0^{\circ} \mathrm{C}\) is mixed with a mass \(m\) of water that has an initial temperature of \(80.0^{\circ} \mathrm{C}\) . No heat is lost to the surroundings. If the final temperature of the system is \(20.0^{\circ} \mathrm{C},\) what is the mass \(m\) of the water that was initially at \(80.0^{\circ} \mathrm{C} ?\)

A carpenter builds an exterior house wall with a layer of wood 3.0 \(\mathrm{cm}\) thick on the outside and a layer of Styrofoam insulation 2.2 \(\mathrm{cm}\) thick on the inside wall surface. The wood has \(k=0.080 \mathrm{W} / \mathrm{m} \cdot \mathrm{K},\) and the Styrofoam has \(k=0.010 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}\). The interior surface temperature is \(19.0^{\circ} \mathrm{C},\) and the exterior surface temperature is \(-10.0^{\circ} \mathrm{C}\) (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

A glass flask whose volume is 1000.00 \(\mathrm{cm}^{3}\) at \(0.0^{\circ} \mathrm{C}\) is completely filled with mercury at this temperature. When flask and mercury are warmed to \(55.0^{\circ} \mathrm{C}, 8.95 \mathrm{cm}^{3}\) of mercury overflow. If the coefficient of volume expansion of mercury is \(18.0 \times 10^{-5} \mathrm{K}^{-1}\) , compute the coefficient of volume expansion of the glass.

You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 \(\mathrm{N}\) . You carefully add \(1.25 \times 10^{4} \mathrm{J}\) of heat energy to the sample and find that its temperature rises 18.0 \(\mathrm{C}^{\circ} .\) What is the sample's specific heat?

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