Temperature, Kinetic Theory, and the Gas Laws

A high-pressure gas cylinder contains $\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{L}$ of toxic gas at a pressure of $\mathbf{1}\mathbf{.}\mathbf{40}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathbf{ }\mathbf{N}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$ and a temperature of $\mathbf{25}\mathbf{.}{\mathbf{0}}^{\mathbf{ }\mathbf{0}}\mathbf{C}$. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature ($\mathbf{-}\mathbf{78}\mathbf{.}{\mathbf{5}}^{\mathbf{ }\mathbf{0}}\mathbf{C}$) to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{atm}$ (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

Question: A high-pressure gas cylinder contains of toxic gas at a pressure of and a temperature of . Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature () to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.40 x 10⁷ N/m² and a temperature of $\mathbf{25}\mathbf{.}\mathbf{0}\mathbf{°}\mathbf{C}$. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature ($\mathbf{-}\mathbf{78}\mathbf{.}\mathbf{5}\mathbf{°}\mathbf{C}$) to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.0 atm  (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

What does it mean to say that two systems are in thermal equilibrium?

Question: What does it mean to say that two systems are in thermal equilibrium?

Give an example of a physical property that varies with temperature and describe how it is used to measure temperature?

Question: Give an example of a physical property that varies with temperature and describe how it is used to measure temperature?

When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down slightly before going up. Explain why?

If you add boiling water to a cup at room temperature, what would you expect the final equilibrium temperature of the unit to be? You will need to include the surroundings as part of the system. Consider the zeroth law of thermodynamics.

Question: If you add boiling water to a cup at room temperature, what would you expect the final equilibrium temperature of the unit to be? You will need to include the surroundings as part of the system. Consider the zeroth law of thermodynamics.

Thermal stresses caused by uneven cooling can easily break glass cookware. Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less susceptible.

Question: Thermal stresses caused by uneven cooling can easily break glass cookware. Explain why Pyrex®, a glass with a small coefficient of linear expansion, is less susceptible.

Water expands significantly when it freezes: a volume increase of about \({\rm{9\% }}\) occurs. As a result of this expansion and because of the formation and growth of crystals as water freezes, anywhere from \({\rm{10\% }}\) to \({\rm{30\% }}\) of biological cells are burst when animal or plant material is frozen. Discuss the implications of this cell damage for the prospect of preserving human bodies by freezing so that they can be thawed at some future date when it is hoped that all diseases are curable

Question: One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion? Explain your answer.

One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion? Explain your answer.

Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.

Liquids and solids expand with increasing temperature because the kinetic energy of a body’s atoms and molecules increases. Explain why some materials shrink with increasing temperature.

Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

Question: Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

Question: A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

How is momentum related to the pressure exerted by a gas? Explain on the atomic and molecular level, considering the behavior of atoms and molecules.

Question: A pressure cooker contains water and steam in equilibrium at a pressure greater than atmospheric pressure. How does this greater pressure increase cooking speed?

Why does condensation form most rapidly on the coldest object in a room-for example, on a glass of ice water

Question: Why does condensation form most rapidly on the coldest object in a room-for example, on a glass of ice water

Question: What is the distinction between gas and vapor?

Question: Why does a beaker of 40.0ºC water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker?

Question: Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?Question: Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?

The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0ºC. What will its height be on a day when the temperature falls to –10.0ºC? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

Oxygen cannot be liquefied at room temperature by placing it under a large enough pressure to force its molecules together. Explain why this is.

What is the distinction between gas and vapor?

Why does a beaker of 40.0ºC water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker?

Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?

What is the Fahrenheit temperature of a person with a 39.0ºC fever

Question: What is the Fahrenheit temperature of a person with a 39.0ºC fever

Frost damage to most plants occurs at temperatures of 28.0ºF or lower. What is this temperature on the Kelvin scale?

Question: Frost damage to most plants occurs at temperatures of 28.0ºF or lower. What is this temperature on the Kelvin scale?

A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?

Question: A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?

The surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?

Question: The surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?

Question: The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0ºC. What will its height be on a day when the temperature falls to –10.0ºC? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble’s.

How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15ºC? Its original height is 321 m and you can assume it is made of steel.

Question: How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15ºC? Its original height is 321 m and you can assume it is made of steel.

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0ºC greater than when they were laid? Their original length is 10.0 m.

Question: How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0ºC greater than when they were laid? Their original length is 10.0 m.

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water  \(1.00{\rm{ km}}\) high for a temperature increase of  \(1.00^\circ {\rm{C}}\) . Note that this calculation is only approximate because ocean warming is not uniform with depth.

Question: Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water   high for a temperature increase of  . Note that this calculation is only approximate because ocean warming is not uniform with depth.

(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0ºC . What is their difference in length at 22.0ºC ? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.

Question: (a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0ºC . What is their difference in length at 22.0ºC? (b) Repeat the calculation for two 30.0-m-long surveyor’s tapes.