# Heat and Thermodynamics

## Specific Heat

The specific heat of a material determines the amount of energy needed to raise its temperature. The energy transfer (Q) needed to raise the temperature (T) by one degree in a solid or liquid with mass (m) and specific heat (c) is given by:

Q = mcΔT

### Molar Specific Heat

Molar specific heat is used when dealing with gases. The heat equation is similar to before, except that the amount of gas is measured in moles, and there are now two equations.

Q = nCVΔT for constant volume Q = nCPΔT for constant pressure

Altering the temperature of a gas must affect either pressure or volume, according to the ideal gas law. If the pressure is kept constant, then increasing temperature will increase the gas's internal energy and do negative work on the gas (further increasing the internal energy), so heat transfer (Q) is greater when pressure is constant. Thus, CP is greater than CV.

The two specific heats are related by the following formulas:

CP - CV = R

CP/CV = γ (Ratio of specific heats). For monatomic gases, γ = 1.67.

## Latent Heat

Heat can cause a phase change in a material (eg. melting). Latent heat is a measure of the heat needed to a substance to change phase.

Q = LΔm

The heat needed to change phase is equal to the latent heat times the mass which is changing phase. The latent heat is unique for each phase change for each material.

## First Law of Thermodynamics

Energy in a system is conserved, so if energy enters or leaves the system, the internal energy must change. Energy may leave the system through work (W) or heat transfer (Q). The change in energy of a system is the sum of heat and work.

ΔEint = Q + W

Note: Heat (Q) and internal energy (Eint) are different, even though both are measured in joules. Heat describes a transfer of energy, while internal energy is the energy of a system when viewed from a reference frame at rest with the system's centre of mass.

## Work and Gases

Work is done when gases change in volume and/or pressure. The work done on a gas is given by the following integral:

W = -ViʃVfPdV

The work done depends on the changes in pressure and volume. If volume is decreasing, then positive work is done on the gas. If volume is increasing, then negative work is done on the gas (positive work is done by the gas).

Work may be visually represented as the area under a pressure-volume curve.

The amount of work depends not only on the starting and finishing points on the curve, but also the path between them. A constant-pressure compression followed by a constant-volume process (1) will do less work than a constant-volume process followed by a constant-pressure compression (2). An arbitrary compression will be somewhere in between (3).

### Isovolumetric Processes

Isovolumetric processes have constant volume throughout. This means that no work is done in an isovolumetric process. The following relations are true in an isovolumetric process:

W = 0 P/T = constant ΔEint = Q = nCVΔT

### Isobaric Processes

Isobaric processes are those which have constant pressure. Generally, heat and work are not zero. The following relations are true in an isobaric process:

T/V = constant Q = nCPΔT

### Constant Temperature

Isothermal processes are those which have constant temperature. The following relations are true in an isothermal process:

PV = constant ΔEint = 0

Adiabatic processes are those in which no heat is transferred. P, V and T all change during an adiabatic process. The following relations are true in an adiabatic process:

Q = 0 PVγ = constant TV(γ-1) = constant ΔEint = W = -PΔV = nCVΔT

In theory, adiabatic processes may be achieved by insulating the walls of the container, or performing the process quickly so no heat is transferred.

## Energy Transfer

### Conduction

Conduction is when thermal energy is transferred through a solid, by the transfer of kinetic energy between particles in that solid. If one part of a solid object is heated, the particles there will gain greater kinetic energy and vibrate more. As they do, they will collide more with nearby particles, transferring kinetic energy. These particles, in turn, will vibrate more and collide with particles near them, spreading the kinetic energy throughout the object. Eventually, even the far ends of the object will receive some of the energy. This increased energy is detectable as an increase in the object's temperature.

The rate of conduction depends on the properties of the substance doing the conducting. Metals are generally good conductors, since they contain free-moving electrons which can transfer heat easily. Gases are poor conductors, because they have a large separation between particles. Materials such as asbestos, glass, paper, fibreglass and wood are also poor thermal conductors.

The rate of conduction depends on the difference in temperature across an object, as well as the properties of the object. Metals, for example, are good thermal conductors since they contain many free-moving electrons with which to transfer heat. Gases also have many free moving particles, but are poor conductors due to the large separation between particles. The law of thermal conduction describes the power transferred by conduction:

P = kA*|dT/dx|

The power transferred (P, measured in Watts) across a width (dx) is the product of thermal conductivity (k), cross-sectional area (A) and temperature gradient (dT/dx).

### Convection

 Convection is the transfer of energy due to the movement of a hot substance.

Forced convection is when the hot substance is moved forcibly by a fan, pump or similar mechanism. Natural convection occurs when the hot substance moves due to a difference in density. A good example of natural convection is hot air rising from a flame or heat source. The hot air expands due to its greater thermal energy, decreasing its density. This lower density causes the hot air to rise above the cooler air, which sinks.

Natural convection tends to set up a convection current. Part of the substance is heated, decreasing its density and causing it to rise away from the heat source. As it does so, the denser substance above it sinks down to the heat source. The initially heated part begins to cool and sink as the denser part below it heats up and rises. This forms a cycle of flow called a convection current.

Radiation is the transfer of heat as electromagnetic waves. Thermal vibration in objects causes them to radiate energy as electromagnetic waves, allowing heat transmission between two objects without an interconnecting medium.

The rate of thermal radiation is described by Stefan's Law:

P = σAeT4

The power transmitted (P) is the proportional to surface area (A), temperature to the power of 4 (T4) and emissivity (e). THe constant of proportionality is σ, which has a value of 5.6696*10-8W/m2.K4.

Emissivity varies from 1 to 0, depending on the object's surface. Matte, dark surfaces tend to have higher emissivity than shiny, bright surfaces.

Emissivity is the same as absorptivity, which measures the fraction of incoming light absorbed by an object. Objects with emissivity (absorptivity) of 1 are called ideal absorbers or black bodies, because they absorb all light which strikes them.

Usually, it is convenient to measure the net energy loss due to radiation, rather than the total energy transmitted, since objects are always absorbing energy radiated from other objects. Stefan's law can be modified to show this:

Pnet = σAe(T4 - T04)

T0 gives the temperature of the object's surroundings, and Pnet gives the net power lost through radiation. For two bodies in thermal equilibrium, Pnet = 0.

## End

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