AP Physics II - Unit 9 - A

The temperature in Kelvin of an ideal gas is directly proportional to…

the average kinetic energy of the gas’ particles

T = …

(2/3)(avg kinetic energy/Boltzmann’s constant)

For an ideal gas, thermal energy is directly proportional to…

temperature

What does N mean?

The number of particles in the sample

What does n mean?

The number of moles in a sample

What does N_A mean?

Avogadro’s number or 6.02 * 10²³ or the number of particles in 1 mole

What does T mean?

The temperature of the sample in Kelvins

What does k_b mean?

Boltzmann’s constant or 1.38 * 10^-23 J/K or the relation of temperature to energy

What does R mean?

Rydberg constant or gas constant or 8.31J/mol K

What is the formula for n?

N/N_A

What is a gas?

A system in which each particle moves freely through space until it collides with another particle or a wall

What is a liquid?

A system in which weak bonds permit motion while keeping particles close together

What is a solid?

A system in which bonds hold particles in a definite shape that can be compressed only slightly

What is the SI unit of volume?

m³

Convert 1 m³ to liters.

1 Liter

Convert 1 cm³ to m³

10^-6 m³

Write the definition of pressure in a gas

p = F/A

What is the SI unit of pressure?

1 pascal or 1 Pa or 1 N/m²

From where is the standard atmosphere or kPa measured?

Sea level

What does psi stand for?

pounds per square inch

What is a vacuum?

An enclosed space with p << 1 atm (NOTE that removing every molecule from a container to make a perfect vacuum is impossible, p = 0 Pa)

When is a net pressure force exerted with a container of gas?

When there is a pressure difference between the two sides of a surface

What is gage pressure, p_g?

The difference between actual pressure and atmospheric pressure

What is pressure in relation to gas temperature?

Directly proportional

What is pressure in relation to container volume?

Inversely proportional

What is pressure in relation to the number of gas particles?

Directly Proportional

What is the ideal gas law?

pV = Nk_bT or pV = nRT

List the properties Ideal-gas processes have.

The quantity of gas is fixed (n is constant), the initial state is defined, and the final state is defined

What is the relation between the initial and final state of an ideal-gas process?

(p_fV_f)/T_f = (p_iV_i)/T_i

What is a trajectory?

An ideal-gas process that changes the state of the gas

Name the ideal-gas process where the volume of the system stays constant.

isochoric

Name the ideal-gas process where the pressure of the system stays constant.

isobaric

Name the ideal-gas process where the temperature of the system stays the same.

isothermal

What is an example of an isochoric process?

Warming a gas in a closed container

What kind of line does an isochoric process appear as on a pV diagram?

A vertical line

What is an example of an isobaric process?

A container with a movable piston that keeps the system in equilibrium

What is an example of an isothermal process?

A container in a larger container with a constant temperature that changes its volume slowly so the sample can transfer heat to a larger container

What is the graph of an isothermal process?

A hyperbola

What is an isotherm?

A graph of an isothermal process

How do you convert Fahrenheit to Celsius?

(5/9)(T_f - 32)

How do you convert Celsius to Fahrenheit?

(9/5)T_c + 32

How do you convert Celsius to Kelvin?

T_c + 273

What are the freezing and boiling points of Celsius?

0 and 100

What are the freezing and boiling points of Fahrenheit?

32 and 212

What does 0K mean?

The average kinetic energy of atoms is zero, and the particles are not moving

Define thermal energy

The total of all kinetic and potential energy of the atoms in an object

Kavg = …

3/2k_bT

E_th = …

3/2Nk_bT

delta E_th= …

3/2nR(deltaT)

What is volume in relation to temperature?

Directly proportional

What is volume in relation to the number of particles?

Directly proportional

What is the root mean square velocity?

The average velocity of a particle in a gas

Vrms = …

sqrt((3kbT)/m)

What relationship is this a graph of?

the relationship between pressure and volume

What relationship is this a graph of?

the relationship between pressure and temperature

What relationship is this a graph of?

the relationship between temperature and volume

What type of process is this PV diagram showing?

an isothermal process

What is the change in T or U, Q, and W? (0, negative, positive, or another value)

0, positive, negative (Q = -W)

What type of process is this PV diagram showing?

an isovolumetric or isochoric process

What is the change in T or U, Q, and W equal to? (0, positive, negative)

positive, positive, 0 (deltaT = Q)

What type of process is this PV diagram showing?

an isobaric process

What is the change in T or U, Q, and W equal to? (0, positive, or negative)

positive, positive, positive (deltaU = Q + PdeltaV)

What type of process is this PV diagram showing?

an adiabatic process

What is the change in T or U, Q, and W equal to? (0, positive, or negative)

positive, 0, positive (adiabats have no heat transfer, deltaU = W)

In a full cycle of a thermodynamic processes, what is the change in T or U, Q, and W equal to? (0, positive, or negative)

0, positive, negative (if V increases then decreases, and vice-versa)

Why can P_iV_i/T_i = P_fV_f/T_f?

Because R is a constant and when n is constant, the gas law formula can be written as PV/T = nR. Therefore PV/T has to be constant, and the initial and final values are equal.

What is the first law of thermodynamics?

When thermal energy (Q) is transferred to a system the internal energy (U) increases or the system does work (like pushing on a piston to expand). Work is only done if the volume changes W = P(deltaV)

How can you calculate work by looking at a PV diagram?

Find the area of the space below the curve.

When work is done on a system, W is … and the gas typically…

positive, compresses

When a system does work, W is … and the gas typically…

negative, expands

What is this a graph of?

A Maxwell-Boltzmann distribution

What does the highest point on the graph represent?

the most probable speed of all the molecules in that system

The pressure of an ideal gas in a closed container…

is equal throughout