Chapter 20 First Law of Thermodynamics

The equivalence between mechanical energy and internal energy

1 cal = 4.186 J. This was determined by experiments performed by James Prescott Joule.

PV diagram

A diagram that shows the relationship between pressure and volume.

Thermal conductivity

A measure of how well a substance conducts internal energy via heat. Substances with high conductivity such as metals have high conductivity values (pg. 584)

Thermal convection

A method of energy transfer. It can be described as the movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat

Thermal radiation

A method of transferring energy via electromagnetic waves

Adiabatic process

A process in which no energy enters or leaves the system via heat. Q=0. In these processes, the change in internal energy is the work done on the system during the process. An adiabatic process can be achieved either by thermally insulating the walls of the system or by performing the process rapidly so that there is negligible time for energy to transfer by heat.

Define quasi-static process

A process that happens infinitely slowly. This allows thermodynamic equilibrium to be maintained at all times

Isobaric process

A process that occurs at constant pressure.

Isothermal process

A process that occurs at constant temperature

Cyclic process

A process that starts and ends at the same state. The change in internal energy is zero so the energy added to the system must equal the negative of the work done on the system

Isovolumetric process

A process that takes place at constant volume

Isolated system

A system that does not exchange energy with it's environment

Calorimetry

A technique for measuring the specific heat of an unknown substance. It involves heating a sample of the unknown substance to some known temperature Tx , placing it in a vessel containing water of known mass and temperature Tw , where Tx>Tw , and measuring the temperature of the water after equilibrium has been reached. Making some assumptions, we can say that the energy transferred away from the sample must be the energy transferred to the water (Qw=-Qs).

What is a state variable?

A variable that depends on the current state of a system, regardless of how the system came to be in its current state. A good example is altitude. The variables on the left side of the conservation of energy equation are all state variables (kinetic, potential, and internal energy).

Define internal energy

All the energy of a system that is associated with its microscopic components—atoms and molecules—when viewed from a reference frame at rest with respect to the center of mass of the system

What is an energy reservoir?

An energy reservoir is a source of energy that is considered to be so great that a finite transfer of energy to or from the reservoir does not change its temperature.

Emmissivity

Equal to the absorptivity, which is the fraction of the incoming radiation that the surface absorbs. Symbolized with an e and ranges from zero to one.

Describe the work done compressing a gas with a cylinder.

For the process of compressing a gas in a cylinder, the work done depends on the particular path taken between the initial and final states. The work done ON the system is the negative of the area under a PV curve. That's why work is a transfer variable.

Relate the work done ON a gas to its pressure and volume using infinitesimals

If the gas is compressed, dV is negative which makes the work positive. If the gas expands, dV is positive and the work is negative. If the volume is constant, dV is zero and the work done on the gas is zero.

Relationship between mechanical energy and internal energy in a system with nonconservative forces

In the presence of non-conservative forces, the mechanical energy of a system decreases and is turned into internal energy. For example a block skidding across a rough, horizontal floor increases in temperature as it's speed is transferred via heat to internal energy

Compare the PV graphs of isobaric, isovolumetric, isothermal, and adiabatic processes.

Isobaric will be a horizontal line. Isovolumetric will be a vertical line. Isothermal will be at a constant temperature so it will fall on an isotherm. An adiabatic process will dive steeper than the isothermal one (pg. 583)

Does Q=0 in an isothermal process?

No. Q≠0. Only the change in temperature is constant (pg. 580)

First Law of Thermodynamics

Notice that it's a special case of the conservation of energy equation (equation 8.2)

Relate Change in energy to mass, specific heat, and change in temperature

Q is the energy transferred by ANY mechanism, m is the mass of the substance that's changing temperature, c is the specific heat, and ∆T is the change in temperature.

Relate the change in internal energy to latent heat

Q is the latent heat times the change in mass

Adiabatic free expansion of gas

Q=0, W=0, so the change in internal energy is zero. That is, the internal energy of the gas does not change in such a process.

Specific heat of common substances at 25°C

Table 20.1

Stefan's law

Tells us the rate at which the surface of an object radiates energy is proportional to the fourth power of the absolute temperature of the surface. P is the power in watts of electromagnetic waves radiated from the surface of the object, s is a constant equal to 5.669 6e-8 W/m²/K⁴, A is the surface area of the object in square meters, e is the emissivity, and T is the surface temperature in kelvins

Differentiate between temperature, heat, and internal energy

Temperature is how we tell if things are in thermal equilibrium with each other. Heat is a energy transfer mechanism. Internal energy is the energy associated with a system's microscopic components. The difference between heat and internal energy is similar to the difference between work and mechanical energy

British thermal unit (Btu)

The amount of energy transfer needed to raise the temperature of a pound of water from 63°F to 64°F

Define calorie

The amount of energy transfer needed to raise the temperature of one gram of water from 14.5°C to 15.5°C. 1 cal= 4.186 J

Define specific heat

The heat capacity per unit mass. Represented with a lowercase c. It's essentially a measurement of how thermally insensitive a substance is to the addition of energy. A better name for this is the specific energy transfer. SI unit of J/(kg*K)

What is the SI unit of internal energy?

The joule. 1J=1Nm

You have one kilogram each of iron glass and water each at 10 °C (a) rank the samples from highest to lowest temperature after 100J of energy is added to each of the samples (b) Rank the samples from greatest to least amount of energy transferred by heat if each sample increases in temperature by 20°C.

The lower the specific heat, the higher the temperature will be after adding energy. So (a) iron, glass, water. The lower the specific heat, the lower amount of energy needed to raise it's temperature by 20°C. So (b) water, glass, iron (quick quiz 20.1 see table 20.1)

Thermal conduction

The process of energy transfer by heat in which energy is transfered via direct molecular collisons. It's Q in EQ 8.2. On the atomic scale, it's an exchange of kinetic energy between microscopic particles in which less energetic particles gain energy in collisions with more-energetic particles. Metals tend to be great thermal conductors while other substances such as asbestos tend to be poor conductors (pg. 583)

What is the total work done on a gas given a volume change?

The work done on a gas in a quasi-static process that takes the gas from an initial state to a final state is the negative of the area under the curve on a PV diagram, evaluated between the initial and final states. We must know how pressure varies with volume.

What is a transfer variable?

They are variables that are associated with changes in the system. They appear on the right side of the conservation of energy equation. An example is heat and work. We cannot determine the values of transfer variables given the initial and final positions of the system.

Law of thermal conduction

This tells us that the rate at which energy is transferred via conduction is proportional to the cross sectional area and the temperature gradient (the rate at which temperature varies with position dT/dx) k is the thermal conductivity constant and has units of W/m/°C (pg. 584)

Define phase change

When substances change their phase. E.g. solid to liquid, liquid to a gas and vice versa. When a substance is undergoing a phase change, such as when ice is melting, energy added to the substance goes into changing the phase instead of raising it's temperature.

Define heat

a process of transferring energy across the boundary of a system because of a temperature difference between the system and its surroundings. It is also the amount of energy Q transferred by this process.

Ideal absorber

an object that absorbs all the energy incident on it, and for such an object, e=1. AKA black body

Define heat capacity

the amount of energy needed to raise the temperature of a substance by 1°C. Represented with a capital C. SI unit of J/K.

Latent heat

the heat required to convert a solid into a liquid or vapor, or a liquid into a vapor, without change of temperature