Exam 13: Temperature and Kinetic Theory

A steel bridge is 1000 m long at $- 20 ^ { \circ } \mathrm { C }$ in winter. What is the change in length when the temperature rises to $40 ^ { \circ } \mathrm { C }$ in summer? The average coefficient of linear expansion of this steel is $11$ $\times 10 ^ { - 6 } K - 1$

A weather balloon containing $2.0 \mathrm {~m} ^ { 3 }$ of hydrogen gas rises from a location at which the temperature is $22 ^ { \circ } \mathrm { C }$ and the pressure is 101 kPa to a location where the temperature is $- 39 ^ { \circ } \mathrm { C }$ and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon?

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is $17 ^ { \circ } \mathrm { C } ?$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A sealed container holds 0.020 moles of ideal nitrogen $\left( \mathrm { N } _ { 2 } \right)$ gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. How many molecules of nitrogen are in the container? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } )$

If the temperature of a gas is increased from $20 ^ { \circ } \mathrm { C } \text { to } 100 ^ { \circ } \mathrm { C }$ by what factor does the rms speed of an ideal molecule change?

Dust particles in a grain elevator frequently have masses of the order of $1.0 \times 10 ^ { - 9 } \mathrm {~kg}$ If, to a first approximation, we model the dust particles as an ideal gas, what would be the rms speed of such a particle in air at $27 ^ { \circ } \mathrm { C } \text { ? }$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A $0.50 \mathrm {~m} ^ { 3 }$ gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of 350 K. The atomic mass of nitrogen is 14.0 g/mol. What is the rms speed of the molecules? (The Boltzmann constant is $\left. 1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } . \right)$

Express a body temperature 98.6°F in Celsius degrees.

At what temperature would the root-mean-square speed of hydrogen, $\mathrm { H } _ { 2 }$ molecules equal 11.2 km/s (the earth's escape speed)? The mass of a hydrogen atom is $1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ and the Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

Consider a flat steel plate with a hole through its center as shown in the figure. When the temperature of the plate is increased, the hole will

The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$ and that of steel is $12 \times 10 ^ { - 6 } K ^ { - 1 }$ At $12 ^ { \circ } \mathrm { C }$ a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. If they are heated together to a higher temperature, which one of the following quantities is closest to the common temperature at which the steel rod will fit snugly in the copper pipe?

Express $- 40 ^ { \circ } \mathrm { C } \text { in } { } ^ { \circ } \mathrm { F } \text {. }$

The coefficient of linear expansion of aluminum is $24.0 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$ and the density of aluminum at $0 ^ { \circ } \mathrm { C } \text { is } 2.70 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 } \text {. }$ What is the density of aluminum at $300 ^ { \circ } \mathrm { C } \text { ? }$

At what temperature would the root mean square speed of oxygen molecules, $\mathrm { O } _ { 2 }$ be 14.0 m/s if oxygen behaves like an ideal gas? The mass of one $\mathrm { O } _ { 2 }$ molecule is $5.312 \times 10 ^ { - 26 } \mathrm {~kg}$ Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

What is the average translational kinetic energy of an ideal gas at 819 K? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A large vat contains 1.000 L of water at $20 ^ { \circ } \mathrm { C }$ What volume will this water occupy when it is heated up to $80 ^ { \circ } \mathrm { C } ?$ Water has a volume expansion coefficient of $210 \times 10 ^ { - 6 } K ^ { - 1 }$

A glass flask has a volume of 500 mL at a temperature of $20 ^ { \circ } \mathrm { C }$ The flask contains 492 mL of mercury at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ The temperature is raised until the mercury reaches the 500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are $18 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ (mercury) and $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (glass) }$

A quantity of mercury occupies $400.0 \mathrm {~cm} ^ { 3 } \text { at } 0 ^ { \circ } \mathrm { C }$ What volume will it occupy when heated to $50 ^ { \circ } \mathrm { C } ?$ Mercury has a volume expansion coefficient of $180 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B . If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures $T _ { A } \text { and } T _ { B }$ in containers A and B, respectively, is

If a certain sample of an ideal gas has a temperature of $104 ^ { \circ } \mathrm { C }$ and exerts a pressure of $2.3$ $\times 10 ^ { 4 } \mathrm {~Pa}$ on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is R=8.31 J/mol x K and Avogadro's number is $N _ { A } = 6.022 \times 10^{23}$ molecules/mol.