## Physics

Thermal Properties

## Big Picture

The thermal properties of matter are described by the laws of thermodynamics. Heat is a form of energy that can be transferred between objects. In physics, “cold” is really just the absence of heat or energy in an object. Heat always flows from hot to cold objects (high temperature to low temperature). Heat, temperature, and all other properties associated with thermal energy come from the random vibrations of atoms and molecules.

## Key Terms

Heat: A form of energy transfer. SI unit: J

Temperature: The temperature of an object is a measurement of the average kinetic energy of the vibrating atoms or molecules. Changes in temperature are the result of the transfer of heat. SI unit: K

Specific Heat: The amount of energy it takes to raise one gram of substance one degree (increase the average kinetic energy). SI units: J/(kg•K)

Thermal Conductivity: How easily a material transmits heat. SI unit: W/(m•K)

Entropy: Entropy is a measure of disorder - increasing entropy increases disorder. Disorder can be thought of how many ways we can rearrange the same system. SI units: J/K

Heat Engine: Turns thermal energy into usable energy.

## Methods of Heat Transfer

Heat naturally flows from areas of high temperature to areas of low temperature. There are three ways that heat can be transferred:

• Conduction: through contact, ex. burning yourself when you touch a hot plate.
• Convection: through movement of regions of a fluid at different temperatures, ex. boiling water.

The specific heat capacity affects how much heat a material can hold.

Thermal conductivity affects the rate heat is transferred. Metals are typically good thermal conductors while air is a poor thermal conductor.

• We experience the effects of thermal conductivity all the time. For example, the air in an oven is at the same temperature as the metal walls, but we only get a burn if we touch the metal walls. This is because the air does not transfer heat to your hand nearly as fast as the metal does.

## Laws of Thermodynamics

• Zeroth: If two systems are the same temperature as a third, then the two systems are the same temperature.
• First: The change in energy of a gas is equal to the change in heat minus the work done by the gas.
• Second: Entropy always increases or stays the same.
In any thermodynamic process, entropy always increases or remains constant. Heat flowing from a hot object to a cold object is an example of increasing entropy because the energy is more evenly distributed and can be “rearranged” in more ways. The universe naturally tends towards disorder until eventually is constantly becoming less ordered and eventually, all energy will be evenly distributed throughout the whole universe.
• Third: Entropy is zero in a perfect crystal at absolute zero.

## Heat Engines

A heat engine (diagram on the right) consists of a hot reservoir ($$T_H$$) and a cold reservoir ($$T_C$$). Energy is added to the system through a heat source, which heats a substance in the engine to a high temperature. The substance then generates work in the body of the engine by transferring heat to the cold reservoir and converting some of this thermal energy into work. However, due to the second law of thermodynamics, it is not 100% efficient.

A Carnot engine is a theoretical engine with the maximum possible efficiency. In a heat engine, there are 4 different ways to change the state of a gas in an engine’s cycle:

• Isothermal: stays at the same temperature
• Isobaric: stays at the same pressure
• Isochoric: stays at the same volume
• Adiabatic: no heat enters or exits the system

Image Credit: Eric Gaba, Public Domain

## Physics

Thermal properties Problem Guide

## Important Equations

$$Q = mcΔT$$

Q - energy/heat

m - mass

c - specific heat

T - temperature

$$W = PΔV$$

W - work

P - pressure

V - volume

$$ΔU = ΔQ - W$$

U - energy

Efficiency = $$1 - \frac{Q_{out}}{Q_{in}}$$

## Sample

### Sample

If you are providing 200 W of power to an engine that is putting out 25 W to an electric heater, what is the efficiency of the engine? How long would it take it to increase the temperature of 15 kg of water by 5°C? The specific heat of water is 4180 J/kg°C.

### Solution

We’ll start by finding the efficiency. For the purpose of efficiency, we can assume that $$Q_{in}$$ is 200 J, and $$Q_{out}$$ is 175 J (200 J - 25 J) because the efficiency of the engine will be constant with time.

Efficiency

=

$$1 - \frac{Q_{out}}{Q_{in}}$$

Efficiency

=

$$1 - \frac{175 J}{200 J}$$

Efficiency

=

$$12.5%$$

Next, for the second part of the problem, we set the amount of energy it take to raise the temperature of the water equal to the power output of the engine multiplied by time.

$$Q$$

=

$$mc \Delta T$$

$$Pt$$

=

$$mc \Delta T$$

set it equal to the engine’s output power multiplied by time

$$t$$

=

$$\frac{mc \Delta T}{P}$$

solve for time

$$t$$

=

$$\frac{15 kg \ \cdot \ 4180 j/kg^{\circ} C \ \cdot \ 5 ^\circ C}{25 W}$$

plug in the known values

$$t$$

=

$$12540 \text{ sec or } 209 \text{ min}$$