PHYS 12B Lecture

What forms of microscopic energy make up internal energy in this lecture?

Eint = Eth + Echem, where Eth is thermal energy and Echem is chemical/configurational energy.

What macroscopic energy changes are usually excluded when studying internal energy here?

Changes in the object's overall kinetic energy and gravitational potential energy.

State the First Law of Thermodynamics using the course sign convention.

ΔEint = Q + W, where W is work done on the system.

What does positive Q mean?

Heat enters the system, increasing its internal energy.

What does negative Q mean?

Heat leaves the system, decreasing its internal energy.

What does positive W mean?

The surroundings do work on the system, usually during compression.

What does negative W mean?

The system does work on its surroundings, usually during expansion.

If Q and W are both positive, what happens to internal energy?

Internal energy increases.

If Q + W = 0, what happens to internal energy?

ΔEint = 0, so the internal energy does not change.

Is ΔEint path-dependent or path-independent?

Path-independent; it depends only on the initial and final states.

Are Q and W individually path-independent?

No. Heat and work can depend on the process used to reach the final state.

What is a state function?

A quantity determined only by the system's current state, not by how it reached that state.

Is internal energy a state function?

Yes; ΔEint depends only on the initial and final states.

What is heat?

Energy transferred microscopically because of a temperature difference.

Does matter contain heat?

No. Matter contains internal or thermal energy; heat is energy being transferred.

What are the units of heat, work, and internal energy?

Joules (J); heat may also be expressed in calories.

In what direction does heat naturally flow?

From higher temperature to lower temperature.

What is thermodynamic work for a gas related to?

Changes in the gas's volume against an external pressure.

What is the general equation for work done on a gas?

W = -∫ from Vi to Vf p dV.

What does the area under a p-versus-V curve represent?

The magnitude of the work; with the course convention, work on the gas is the negative of the signed area under the curve.

Why is there a negative sign in W = -∫p dV?

Expansion gives ΔV > 0 but means the gas does work, so work done on the gas is negative.

What sign does work have when a gas expands?

W < 0 because the gas does work on its surroundings.

What sign does work have when a gas is compressed?

W > 0 because the surroundings do work on the gas.

What is a quasi-static process?

A sufficiently slow process in which the system remains close to equilibrium at every stage.

What is the work done on a gas during a constant-volume process?

W = 0 because ΔV = 0.

What is the work done on a gas during a constant-pressure process?

W = -pΔV.

Under what condition can W = -pΔV be used directly?

When the pressure remains constant throughout the process.

For constant-pressure expansion, what is the sign of W?

Negative because ΔV > 0.

For constant-pressure compression, what is the sign of W?

Positive because ΔV < 0.

What is an isothermal process?

A process that occurs at constant temperature.

What relationship holds for an ideal gas during an isothermal process?

pV = constant, assuming the number of gas particles stays constant.

What is the work done on an ideal gas during an isothermal process?

W = -nRT ln(Vf/Vi).

For isothermal expansion, what sign does W = -nRT ln(Vf/Vi) have?

Negative because Vf/Vi > 1 and the logarithm is positive.

For isothermal compression, what sign does W have?

Positive because Vf/Vi < 1 and the logarithm is negative.

What shape does an isothermal curve have on a pV diagram?

A decreasing inverse curve described by p = nRT/V.

How can the temperature of a point on a pV diagram be calculated?

T = pV/(nR).

For the same amount of ideal gas, which pV point has the higher temperature?

The point with the larger product pV.

What is the ideal-gas law?

pV = nRT.

What units must be used in the ideal-gas law?

Pressure in Pa, volume in m³, temperature in K, and amount in mol when R = 8.31 J/(mol·K).

What is the microscopic form of the ideal-gas law?

pV = NkBT.

How are the number of particles and number of moles related?

n = N/NA.

What are the values of Avogadro's number and Boltzmann's constant?

NA = 6.022 × 10²³ particles/mol and kB = 1.38 × 10⁻²³ J/K.

How do you convert cubic centimeters to cubic meters?

1 cm³ = 10⁻⁶ m³, so 1,000 cm³ = 1.00 × 10⁻³ m³.

How do you convert atmospheres to pascals?

Multiply by 1.013 × 10⁵ Pa/atm.

An ideal gas has p = 1.7 atm, V = 1,000 cm³, and N = 1.4 × 10²³ particles. How many moles are present?

n = N/NA = (1.4 × 10²³)/(6.022 × 10²³) ≈ 0.232 mol.

For that gas, what are pressure and volume in SI units?

p = 1.722 × 10⁵ Pa and V = 1.00 × 10⁻³ m³.

For that gas, what is its temperature in kelvin?

T = pV/(nR) ≈ 89.3 K.

What is 89.3 K in degrees Celsius?

TC = T - 273.15 = -183.9°C, approximately -184°C.

What is the equation for linear thermal expansion?

ΔL = αLΔT.

What does α represent?

The coefficient of linear expansion, usually measured in K⁻¹.

What factors determine the change in an object's length?

The coefficient α, original length L, and temperature change ΔT.

What usually happens to a solid when its temperature increases?

It expands because its atoms move farther apart on average.

Why does a bimetallic strip bend when heated?

The two attached metals have different expansion coefficients, so one expands more than the other.

How can a bimetallic strip be used in a thermostat?

Its bending can open or close an electrical circuit as temperature changes.

What is the equation for volume expansion?

ΔV = βVΔT.

What does β represent?

The coefficient of volume expansion.

For an isotropic solid, how are β and α related?

β = 3α.

Why is volume expansion especially useful for liquids?

A liquid has no fixed shape, so changes in volume are more meaningful than changes in length.

What is unusual about water's thermal expansion?

Water reaches its maximum density near 4°C rather than at 0°C.

Why does ice float in liquid water?

Ice is less dense than liquid water, so the buoyant force can support it.

What happens to the water level when a dense iron object is moved from a floating block into the water and sinks?

The water level decreases because the sinking iron displaces only its volume instead of an amount of water equal to its weight.

What is a common mistake in First Law problems?

Using the wrong sign for work; this course defines positive W as work done on the system.

What is a common mistake when finding work from a pV diagram?

Forgetting that work depends on the entire path and corresponds to the area under the curve.

What is a common mistake in ideal-gas calculations?

Using Celsius, atm, or cm³ without converting to K, Pa, and m³ when using SI units.