Exam 13: Temperature and the Ideal Gas

The density of copper at $293 \mathrm{~K}$ is $8,940 \mathrm{~kg} / \mathrm{m}^{3}$ and its linear expansion coefficient is $17.0 \times 10^{-6} \mathrm{~K}^{-1}$ . Consider a hot cube of copper that is $1.0 \mathrm{~cm}$ on a side when its temperature is $1.356 \mathrm{~K}$ . What is the cube's mass?

A $3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}$ rectangular piece of copper is at a temperature of $10.0^{\circ} \mathrm{C}$ . The coefficient of linearexpansion of copper is $17.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature of the copper rectangle increases by $2.00^{\circ} \mathrm{C}$ , thenwhat is its change in area?

The diffusion constant for oxygen diffusing through tissue is $1.0 \times 10^{-11} \mathrm{~m} 2 / \mathrm{s}$ . In a certain sample oxygen diffuses through the tissue at a rate of $2.0 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$ . If the thickness of the tissue is doubled, then what is the rate of oxygen flow through the tissue?

A sample of an ideal gas has a volume of $0.0100 \mathrm{~m}^{3}$ , a pressure of $100 \times 10^{3} \mathrm{~Pa}$ , and a temperature of 300 $\mathrm{K}$ . What is the number of moles in the sample of gas?

The mean free path for a nitrogen molecule in a tank of dry nitrogen at $273 \mathrm{~K}$ is $0.15 \mu \mathrm{m}$ . If the diameter of a nitrogen molecule is $0.29 \mathrm{~nm}$ , what is the pressure in the tank?

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm})$ . What is the mean free path if the pressure of the gas is doubled but the temperature is constant?

A sample of water has a mass of 10.0 grams. What is the number of molecules of water in the sample? $(\mathrm{H}=$ $1 \mathrm{u}, \mathrm{O}=16 \mathrm{u}$ , and $1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{~kg}$ .)

ideal gas has a pressure of $2.5 \mathrm{~atm}$ , a volume of $1.0 \mathrm{~L}$ at a temperature of $30^{\circ} \mathrm{C}$ . How many molecules are there in the gas?

One mole of carbon- 12 has a mass of 12.00 grams. What is the mass of a ${ }^{12} \mathrm{C}$ atom?

What is the average kinetic energy per particle in 1.00 mole of an ideal gas at a pressure of 1.50 atmospheres and a temperature of $20^{\circ} \mathrm{C}$ ?

$147.5 \mathrm{ml}$ of ethyl alcohol (coefficient of volume expansion $\beta=1,120 \times 10^{-6} \mathrm{~K}^{-1}$ ), at a temperature of 273.1 $\mathrm{K}$ , is poured into a $150.0 \mathrm{ml}$ glass beaker (whose coefficient of volume expansion is negligible by comparison). To what temperature does the beaker have to be warmed for it to be completely full (i.e., for the volume of the alcohol to reach $150.0 \mathrm{ml})$ ?

Abrass rod is $25.0 \mathrm{~cm}$ long at a temperature of $20.0^{\circ} \mathrm{C}$ . The coefficient of linear expansion of brass is $19.0 \times$ $10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature changes to $25^{\circ} \mathrm{C}$ , then the increase in length of the brass rod is

A brass plate measures $30.0 \mathrm{~cm}$ by $40.0 \mathrm{~cm}$ . The coefficient of linear thermal expansion is $19.0 \times 10^{-6 /{ }^{\circ} }\mathrm{C} \text {. }$ If the temperature of the plate is increased by $10.0 \mathrm{~K}$ , then what is the increase in the area of the plate?

What is the average kinetic energy per particle in 1.00 mole of an ideal gas at a pressure of 1.50 atmospheres and a volume of 2.00 liters?

The mass density of normal air at a certain temperature is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ . If the average molecular mass of air is $29.0 \mathrm{u}$ , how many air molecules are in spherical balloon of radius $15.0 \mathrm{~cm}$ ?

An sample of helium occupies $44.8 \mathrm{~L}$ at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ . What is the mass of the sample? The atomic mass of helium is $4.00 \mathrm{u}$ .

An ideal gas composed of helium atoms is at a pressure of 2.00 atmospheres and a temperature of $35.0^{\circ} \mathrm{C}$ . What is the mass density? $(\mathrm{He}=4.00 \mathrm{u})$

An aluminum rod is $20.0 \mathrm{~cm}$ in length, has a diameter of $10.0 \mathrm{~mm}$ and is at a temperature of $20^{\circ} \mathrm{C}$ . The coefficient of linear expansion of aluminum is $23.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature changes to $50^{\circ} \mathrm{C}$ , then the increase in diameter of the aluminum rod is

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm})$ . What is the mean free path if the pressure of the gas is doubled and the temperature is tripled?

An ideal gas is at a temperature of $30^{\circ} \mathrm{C}$ and a pressure of 2.00 atmospheres. What is the number of particles per unit volume of the gas?