PHYS 12D Lecture

What is specific heat capacity?

The heat needed to raise the temperature of 1 kg of a substance by 1 K (or 1°C).

Specific heat equation

Q = mcΔT = mc(Tf − Ti)

What does each symbol in Q = mcΔT mean?

Q is heat transferred (J); m is mass (kg); c is specific heat (J/kg·K); ΔT is the temperature change (K or °C).

How do you find an object's temperature change?

ΔT = Tf − Ti

What does positive Q mean?

Heat enters the system.

What does negative Q mean?

Heat leaves the system.

What does a high specific heat mean?

The substance needs a lot of heat to change its temperature; water has a high specific heat.

How does the specific heat of most metals compare with water?

Metals generally have lower specific heat than water, so they warm or cool more with the same heat transfer.

Can heat transfer change something besides temperature?

Yes. Heat can change an object's phase or transfer energy that contributes to work.

What is latent heat (heat of transformation)?

The energy per unit mass needed to complete a phase change.

Latent heat equation

Q = mL

What does each symbol in Q = mL mean?

Q is heat transferred (J); m is the mass that changes phase (kg); L is the latent heat (J/kg).

Why is latent heat called “latent”?

The energy changes the substance's phase rather than its temperature, so the temperature does not show that energy change.

What is heat of fusion?

The latent heat for a solid-to-liquid phase change.

What is heat of vaporization?

The latent heat for a liquid-to-gas phase change.

What happens to temperature during a phase change of a pure substance?

It stays constant while the phase change is occurring, even though heat is transferred.

How do you calculate heat for a process with multiple stages?

Calculate Q for each warming, cooling, or phase-change stage, then add the signed heat transfers.

What is calorimetry?

A method for measuring heat transfer by placing materials in thermal contact and measuring their temperature changes.

What is a calorimeter?

A device where heat transfers between materials in an ideally isolated system.

What does an isolated calorimetry system imply?

Energy does not enter or leave the combined system, so heat lost by one part is gained by another.

Calorimetry energy-balance equation

Qnet = Q1 + Q2 + … = 0 for an isolated system.

How do you find the final temperature in a basic two-object calorimetry problem?

Write Q for each object using its own mass, specific heat, and temperature change; set the sum of the Q values to zero; solve for Tf.

What is the sign of Q for an object that cools down?

Negative, because its final temperature is lower than its initial temperature.

What is the sign of Q for an object that warms up?

Positive, because its final temperature is higher than its initial temperature.

How do you handle a calorimetry problem that may involve boiling or melting?

Check whether the heat needed to reach the phase-change temperature is available; if so, include a Q = mL stage.

Ice at −10°C becomes liquid water at 0°C: what stages are involved?

Warm the ice from −10°C to 0°C, then melt it at 0°C.

About how much heat changes 0.20 kg of ice at −10°C into water at 0°C?

About 70,000 J: roughly 4,200 J to warm the ice plus 66,000 J to melt it.

What is internal (thermal) energy in the lecture’s simplified model?

Eint = mcT, using absolute temperature in kelvin; for a temperature change, use ΔEint = mcΔT.

What is the First Law of Thermodynamics convention used in these slides?

ΔEint = Q + W, where Q is heat added to the system and W is work done on the system.

If heat is added but the temperature stays constant, must the First Law be violated?

No. The added heat can be transferred into work instead of increasing internal energy.

What is a state variable?

A property determined by the system’s state, not by the path used to reach that state.

Which quantities in the slides are state variables?

Pressure, volume, temperature, internal energy, and enthalpy.

Are heat Q and work W state variables?

No. Their values depend on the path taken between states.

If a gas goes from state A to state C by two different paths, which properties have the same changes?

State variables have the same changes because the initial and final states are the same.

Can Q and W differ for two paths with the same initial and final states?

Yes. Heat and work depend on the path.

What is a complete cycle on a pV diagram?

A process that returns the system to its initial state.

What is the net change in a state variable over a complete cycle?

Zero, because the system ends in the same state where it began.

Must net heat Q and work W each be zero over a complete cycle?

No. They can be nonzero even though the net change in state variables is zero.

What is enthalpy?

A state variable defined as H = Eint + pV.

What is the SI unit of enthalpy?

The joule (J).

Is enthalpy conserved like energy?

No. Enthalpy is a state variable, but it is not a conserved quantity.

What is special about enthalpy change at constant pressure?

For the constant-pressure process described in the slides, ΔH = Q.

Why is enthalpy useful for constant-pressure processes?

Because the enthalpy change can be measured as the heat transferred at constant pressure.

How is the heat of fusion related to enthalpy of fusion at constant pressure?

They are numerically equivalent for a constant-pressure phase change.

How is the heat of vaporization related to enthalpy of vaporization at constant pressure?

They are numerically equivalent for a constant-pressure phase change.

In the horseshoe example, why does some water boil away?

The hot iron releases enough heat to warm the water to 100°C and then vaporize part of it.