Thermal energy is the total energy associated with the motion of the particles in matter. Thermal energy or heat (Q) is measured in the units of energy (Joules).
Heat can be transported from place to place by radiation, convection, and conduction.
The specific heat (c) of a substance is a measure of the material's ability to absorb and store heat. (see table 12-1) Specific heat has the unit J/Kg °C.
The heat required to raise or lower the temperature of an object is computed by using the equation: Q = m c ΔT where m is the mass of the object (measured in kg), c is the specific heat of the substance, and ΔT is the change in the temperature (T2 - T1).
The law of heat exchange states that the heat that is lost by a warm object, w, is equal to the heat that is gained by a colder object, d. Equation: mw cw ΔTw = md cd ΔTd where m is the mass of the object (measured in kg), c is the specific heat of the substance, and ΔT is the change in the temperature (T2 - T1).
Change of state requires energy. This energy when put in, breaks bonds or when removed, allows the bonds to form thus effecting a change of state. The heat involved in the solid-liquid state change is called the latent heat of fusion. The heat involved in the liquid gas state change is called the latent heat of vaporization. (see table below) The heats of fusion and vaporization have the unit of J/Kg
In order to compute the heat required to effect a change of state, the sample must be at the freezing point or boiling point of the substance. If the sample is Not, heat must be put in (or removed) before the change of state can occur. See heat required to raise or lower the temperature of an object above. After the freezing point has been reached, use: Q = m Hf, where Hf is the latent heat of fusion. After the boiling point has been reached, use: Q = m Hv, where Hv is the latent heat of vaporization.
Thermal expansion and contraction is the change in some dimension of a solid or liquid as a result of a change in the temperature of the material. In this unit we will consider linear expansion and contraction (changing the length of a solid body). Equation: Δl = α l ΔT where Δl is the change in the length of the object, l is the original length of the object, ΔT is the change in temperature, and α is the coefficient of linear expansion (see table below). In addition, liquids undergo volume expansion and contraction (changing the volume of the liquid). Equation: ΔV = β V ΔT where ΔV is the change in the volume of the liquid, β is the coefficient of volume expansion, V is the original volume of the liquid, and ΔT is the change in temperature.
Thermodynamics is the Name given to the study of processes in which energy is transferred as heat and work.
Heat is the transfer of energy due to differences in temperature where work is the transfer of energy by other means.
A system is any object or set of objects considered in a thermodynamic calculation. The remainder of the universe is referred to as the environment.
An open system is one, which allows the transfer of matter and energy to and from the environment.
A closed system only allows the transfer of energy to the environment, but Not matter. The total matter in a closed system is constant.
An isolated system is a closed system in which there is No energy transfer to the environment whatsoever.
The internal energy (U) is the sum total of all the energies associated with the constituent particles in a system.
The first law of thermodynamics is a special case of the law of conservation of energy. The first law states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work done by the system (W). ΔU = Q –W
Adiabatic processes are processes in which there is Not exchange of heat with the environment (ΔQ = 0).
Isothermal processes are processes in which the temperature remains constant. If a gas expands isothermally against a pressure the change in the internal energy is zero and any heat added equals the external work done by the gas.
Isobaric processes are processes in which the pressure of a gas remains constant.
Isochoric processes (isovolumetric) are processes in which the volume of a confined gas in a system remains constant.
The second law of thermodynamics is concerned with the fact that certain processes are irreversible. This irreversibility points to several statements of the second law.
The Clausius statement: Heat flows Naturally from a hot object to a cold object; heat will Not flow spontaneously from cold objects to hot objects.
The Kelvin-Planck statement: No device is possible whose sole effect is to transform a given amount of heat completely to work.
The entropy statement of the second law is stated two ways: The total entropy (disorder) of a system plus that of its environment always increases as the result of any Natural process. Natural processes always move toward a state of maximum disorder. Well-ordered mechanical energy degrades spontaneously to less ordered thermal energy.
Information theory is also concerned with the increase in entropy stated by the second law. Well-ordered systems contain more information than less ordered ones. A consequence of the increase of entropy is a corresponding decrease in the information carried by that system.
The force required to break a rod or wire is called the breaking strength. The breaking strength of a given rod or wire is independent of its length. Use the breaking strength equation to compute its value: BS = (TS) (A) where TS is the tensile strength of the material and A is the cross sectional area in m2
Elasticity is that property by virtue of which a body tends to return to its original size or shape after a deformation and when the deforming forces have been removed.
Stress is the force per unit area, which can cause a deformation. As in the discussion above for thermal effects, here we will only consider longitudinal (lengthwise) elasticity. Stress = F / A where F is the stretching force in Newtons and A is the cross sectional area in m2. Stress has the unit N/m3.
Strain is the fractional deformation caused by stress. Strain = Δl / l where Δl is the elongation and l is the original length. The strain is a pure number and has no units.
The Modulus of Elasticity is the ratio of Stress/Strain. It is the slope of the graph of Stress ploted verses Strain, commonly refereed to as Hooke's Law. The modulus of elasticity for linear elasticity is called Young's modulus. The equation for Young's modulus is: Y = F l / Δl A. Where F is the stretching force (in Newtons), l is the original length (in m), Δl is the elongation (in m), and A is the cross sectional area (m2).
|METAL|| Tensile Strength (x108)
| Young's Modulus (x1010)
cice = 2060
csteam = 2020
cwater = 4180
cAl = 906
cglass = 664
Qf for water = 3.34 x 105
Qv for water =2.26 x 106
|Material|| Coefficient of linear expansion
(α) ( x 10-6)
| Coefficient of volume expansion
(β) ( x 10-6)
L = 2.000 m
d = 0.0400 mm
xs area = ________m2
|Force (N)||Δ l (m x 10-4)||Stress x 109 (N/m2)||Strain x 10-4|
Use the values for tensile strength and Young's modulus from the previous problem sheet.
William Dietsch posted & edited 5 February 2008 by D Trapp