Exam 13: Temperature and Kinetic Theory

The density of water at $0 ^ { \circ } \mathrm { C }$ is $999.84 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and at $4 ^ { \circ } \mathrm { C }$ it is $999.96 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ A 1.0-L container, full to the brim with water at $4.0 ^ { \circ } \mathrm { C }$ is placed in the refrigerator. By the time that the temperature of the water reaches $0.0 ^ { \circ } \mathrm { C }$ what volume of water has spilled from the container, assuming that the contraction of the container is negligible?

A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-mean-square speed of its molecules was originally v, what is the new root-mean-square speed?

Your lungs hold 4.2 L of air at a temperature of $27 ^ { \circ } \mathrm { C }$ and a pressure of 101.3 kPa. How many moles of air do your lungs hold? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A 3.9-L volume of ideal neon gas (monatomic) is at a pressure of 5.6 aym and a temperature of 330 K. The atomic mass of neon is 20.2 g/mol . The temperature of the gas is now increased to 430 K and the volume is increased to 5.9 L. What is the final pressure of the gas?

As shown in the figure, an air pocket at the top of a vertical tube, closed at the upper end and open at the lower, occupies a volume of $560 \mathrm {~cm} ^ { 3 }$ at the surface of a lake where the air pressure is $1.0 \times 10 ^ { 5 } \mathrm {~Pa}$ and the temperature is $37 ^ { \circ } \mathrm { C }$ What is the volume of the air in the pocket if the tube is taken to a depth of 56 meters, where the temperature is $7 ^ { \circ } \mathrm { C } ?$ Assume that none of the air escapes from the tube. The density of the water in the lake is 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$

The coefficient of volume expansion of a certain olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K}^{ - 1}$ A 1.0 -L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by $25 \mathrm { C } ^ { \circ }$ As a result, 0.0167 L of olive oil spills over the top of the beaker. Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made?

The temperature in your classroom is closest to

If the temperature of an ideal gas is increased from $20 ^ { \circ } \mathrm { C } \text { to } 40 ^ { \circ } \mathrm { C }$ by what percent does the speed of the molecules increase?

Suppose that a rigid aluminum wire were to be strung out in a loop that just fits snugly around the equator (assuming a perfectly spherical Earth with a radius of $\left. 6.37 \times 10 ^ { 6 } \mathrm {~m} \right)$ If the temperature of the wire is increased by $0.50 ^ { \circ } \mathrm { C }$ and the increase in length is distributed equally over the entire length, how far off the ground will the wire loop be if it remained centered on the earth? The coefficient of linear expansion of aluminum is $24 \times 10 ^ { - 6 } K ^ { - 1 }$

How many moles are there in 2.00 kg of copper? The atomic weight of copper is 63.5 g/mol and its density is $8.90 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K^{ - 1}$ 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. Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe?

A sealed cylinder fitted with a movable piston contains ideal gas at $27 ^ { \circ } \mathrm { C }$ pressure $0.500 \times 10 ^ { 5 } \mathrm {~Pa}$ and volume $1.25 \mathrm {~m} ^ { 3 }$ What will be the final temperature if the gas is compressed to $0.800 \mathrm {~m} ^ { 3 }$ the pressure rises to $0.820 \times 10 ^ { 5 } \mathrm {~Pa} ?$

A laboratory vacuum pump can reduce the pressure in a chamber to $1.0 \times 10 ^ { - 7 } \mathrm {~Pa}$ If the volume of the chamber is $0.500 m ^ { 3 }$ and the temperature is $27 ^ { \circ } \mathrm { C }$ how many molecules are left inside chamber? $\left( N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } , R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } \right)$

A hole in a brass plate has a diameter of 1.200 cm at $20 ^ { \circ } \mathrm { C }$ What is the diameter of the hole when the plate is heated to $220 ^ { \circ } \mathrm { C } ?$ The coefficient of linear thermal expansion for brass is $19 \times 10 ^ { - 6 } K ^ { - 1 }$

A $0.40 - \mathrm { m } ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the pressure of the gas? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} =$ $101 \text { kPa) }$

An aluminum rod 17.400 cm long at $20 ^ { \circ } \mathrm { C }$ is heated to $100 ^ { \circ } \mathrm { C }$ What is its new length? Aluminum has a linear expansion coefficient of $25 \times 10 ^ { - 6 } K ^ { - 1 }$

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44.0 g/mole, is 396 m/s. What is the rms speed of water vapor molecules, with a molecular weight of 18.0 g/mol, at the same temperature as the carbon dioxide?

A 20.0-L pressure vessel holds 2.00 mol of oxygen at $30 ^ { \circ } \mathrm { C }$ What is the pressure inside the vessel? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

A mercury thermometer has a glass bulb of interior volume $0.100 \mathrm {~cm} ^ { 3 } \text { at } 10 ^ { \circ } \mathrm { C }$ The glass capillary tube above the bulb has an inner cross-sectional area of $0.012 \mathrm {~mm} ^ { 2 }$ . The coefficient of volume expansion of mercury is $1.8 \times 10 ^ { - 4 } K ^ { - 1 }$ . If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from $5 ^ { \circ } \mathrm { C } \text { to } 35 ^ { \circ } \mathrm { C }$ if the bulb was full at $5 ^ { \circ } \mathrm { C } ?$ ?

Originally 2.00 mol of gas are at STP. If the temperature changes to $47.0 ^ { \circ } \mathrm { C }$ and the pressure decreases to half of what it was, how many liters do the two moles now occupy? (1 atm=101 kPa, R=8.31 J/mol . K)