Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Question: (II) An ordinary glass is filled to the brim with 450.0 mL of water at 100.0°C. If the temperature of glass and water is decreased to 20.0°C, how much water could be added to the glass?

The volume of water that can be added to the glass container is \(6.59{\rm{ mL}}\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of given data

The coefficient of volumetric expansion of glass is \({\beta _{{\rm{Glass}}}} = 27 \times {10^{ - 6}}\;{\rm{/^\circ C}}\).
The coefficient of volumetric expansion of water is \({\beta _{{{\rm{H}}_{\rm{2}}}{\rm{O}}}} = 210 \times {10^{ - 6}}\;{\rm{/^\circ C}}\).
The initial volume of both water and container is \({V_{{\rm{iGlass}}}} = {V_{{\rm{i}}{{\rm{H}}_{\rm{2}}}{\rm{O}}}} = {V_{\rm{i}}}\).
The initial volume of glass and water is \({V_{\rm{i}}} = 450{\rm{ mL}}\).
The final decreased temperature is \({T_f} = 20^\circ {\rm{C}}\).
The initial temperature of glass and water is \({T_i} = 100^\circ {\rm{C}}\).

Step 2: Understanding the variation in the volume of water

The initial volume of water is equal to that of the glass container.

The volume of water added to the glass container is obtained by subtracting the final volume of water from the final volume of the glass container.

Step 3: Determination of the volume of water added to the glass container

The volume of water that can be added to the glass container can be expressed as shown below:

\(\begin{aligned}{c}{V_{{\rm{add}}}} &= {\left( {{V_i} + \Delta V} \right)_{{\rm{Glass}}}} - {\left( {{V_i} + \Delta V} \right)_{{{\rm{H}}_{\rm{2}}}{\rm{O}}}}\\ &= \Delta {V_{{\rm{Glass}}}} - \Delta {V_{{{\rm{H}}_{\rm{2}}}{\rm{O}}}}\\ &= {\beta _{{\rm{Glass}}}}{V_{{\rm{iGlass}}}}\Delta T - {\beta _{{{\rm{H}}_{\rm{2}}}{\rm{O}}}}{V_{{\rm{i}}{{\rm{H}}_{\rm{2}}}{\rm{O}}}}\Delta T\\ &= \left( {{\beta _{{\rm{Glass}}}} - {\beta _{{{\rm{H}}_{\rm{2}}}{\rm{O}}}}} \right){V_{\rm{i}}}\left( {{T_f} - {T_i}} \right)\end{aligned}\)

Substitute the values in the above equation.

\(\begin{aligned}{c}{V_{{\rm{add}}}} &= \left( {27 \times {{10}^{ - 6}}\;{\rm{/^\circ C}} - 210 \times {{10}^{ - 6}}\;{\rm{/^\circ C}}} \right) \times 450{\rm{ mL}} \times \left( {20^\circ {\rm{C}} - 100^\circ {\rm{C}}} \right)\\ &= \left( { - 183 \times {{10}^{ - 6}}\;{\rm{/^\circ C}}} \right) \times 450{\rm{ mL}} \times \left( { - 80^\circ {\rm{C}}} \right)\\ &= 6.59{\rm{ mL}}\end{aligned}\)

Thus, the volume of water that can be added to the glass container is \(6.59{\rm{ mL}}\).

Find Study Materials for

Create Study Materials

Select your language

Physics Principles with Applications

Answers without the blur.

Short Answer

Question: (II) An ordinary glass is filled to the brim with 450.0 mL of water at 100.0°C. If the temperature of glass and water is decreased to 20.0°C, how much water could be added to the glass?

Step by Step Solution

Step 1: Identification of given data

Step 2: Understanding the variation in the volume of water

Step 3: Determination of the volume of water added to the glass container

Most popular questions for Physics Textbooks

Question: The density of gasoline at 0°C is \(0.68 \times {10^3}\;{\rm{kg/}}{{\rm{m}}^3}\). (a) What is the density on a hot day, when the temperature is 33°C? (b) What is the percent change in density?

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics Principles with Applications

Answers without the blur.

Short Answer

Question: (II) An ordinary glass is filled to the brim with 450.0 mL of water at 100.0°C. If the temperature of glass and water is decreased to 20.0°C, how much water could be added to the glass?

Step by Step Solution

Step 1: Identification of given data

Step 2: Understanding the variation in the volume of water

Step 3: Determination of the volume of water added to the glass container

Most popular questions for Physics Textbooks

Question: The density of gasoline at 0°C is \(0.68 \times {10^3}\;{\rm{kg/}}{{\rm{m}}^3}\). (a) What is the density on a hot day, when the temperature is 33°C? (b) What is the percent change in density?

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics