HEAT

INTENDED LEARNING OUTCOMES

• Identify the factors that affect thermal expansion and thermal stress.• Describe different mechanism of heat transfer.• Explain the concepts involved in calorimeters

such as specific heat and latent heat.• Determine the heat absorbed or given off given

specific situation.• Solve other sample problems related to thermal

expansion, thermal stress and heat transfer and calorimetry.

CONCEPTS

• Heat is defined as the transfer of energy across the boundary of a system due to a temperature difference between the system and its surroundings.

• When you heat a substance, you are transferring energy into it by placing it in contact with surroundings that have a higher temperature.

• Calorie (cal), which is defined as the amount of energy transfer necessary to raise the temperature of 1 g of water from 14.5°C to 15.5°C.1 (The “Calorie,” written with a capital “C” and used in describing the energy content of foods, is actually a kilocalorie.)

• The unit of energy in the U.S. customary system is the British thermal unit (Btu), which is defined as the amount of energy transfer required to raise the temperature of 1 lb of water from 63°F to 64°F.

• The joule has already been defined as an energy unit based on mechanical processes.

THERMAL EXPANSION AND THERMAL STRESS

• Thermal expansion is a consequence of the change in the average separation between the atoms in an object. If thermal expansion is sufficiently small relative to an object’s initial dimensions; the change in any dimension is, to a good approximation, proportional to the first power of the temperature change.

THERMAL EXPANSION AND THERMAL STRESS

• Suppose an object has an initial length Li along some direction at some temperature and the length increases by an amount ∆L for a change in temperature ∆T. Because it is convenient to consider the fractional change in length per degree of temperature change, we define the average coefficient of linear expansion as

THERMAL EXPANSION AND THERMAL STRESS

• Experiments show that is constant for small changes in temperature. For purposes of calculation, this equation is usually rewritten as

where Lf is the final length, Ti and Tf are the initial and final temperatures, respectively, and the proportionality constant is the average coefficient of linear expansion for a given material and has units of (°C) - 1.

THERMAL EXPANSION AND THERMAL STRESS

• Because the linear dimensions of an object change with temperature, it follows that surface area and volume change as well. The change in volume is proportional to the initial volume Vi and to the change in temperature according to the relationship

∆V = ßV0∆T

Where ß is the average coefficient of volume expansion.

THERMAL EXPANSION AND THERMAL STRESS

• Thermal Stress – an internal stress created when temperature deformation (expansion/contraction) is not permitted to occur freely.

SAMPLE PROBLEM

1. A steel railroad track has a length of 30.000 m when the temperature is 0 C. What is the length on a hot day when the temperature is 40.0. The linear coefficient of steel is .

2. A circular copper ring at 20.0 has a hole with an area of 9.980 . What minimum temperature must it have so that it can be slipped onto a steel having a cross sectional area of 10.000 . The linear coefficient of copper is

HEAT TRANSFER

• Heat transfer - study of the exchange of thermal energy through a body or between bodies which occurs when there is a temperature difference.

• When two bodies are at different temperatures, thermal energy transfers from the one with higher temperature to the one with lower temperature. Heat always transfers from hot to cold.

HEAT TRANSFER

 

Units and Conversion Factors for Heat Measurements

  SI Units English Units

Thermal Energy (Q) 1 J 9.4787×10-4 Btu

Heat Transfer Rate (H) 1 J/s or 1 W 3.4123 Btu/h

Heat Flux (h’) 1 W/m2 0.3171 Btu/h ft2

MECHANISMS OF HEAT TRANSFER

• Conduction is the transfer of heat through solids or stationery fluids. Two mechanisms explain how heat is transferred by conduction: lattice vibration and particle collision

MECHANISMS OF HEAT TRANSFER

Conduction by lattice vibration

MECHANISMS OF HEAT TRANSFER

Conduction by particle collision

MECHANISMS OF HEAT TRANSFER

The effectiveness by which heat is transferred through a material is measured by the thermal conductivity, k. A good conductor, such as copper, has a high conductivity; a poor conductor, or an insulator, has a low conductivity. Conductivity is measured in watts per meter per Kelvin (W/mK).

The rate of heat transfer by conduction is given by:

x

TkA

t

QH conduction

where: A = cross-sectional area through which the heat is conducting,

MECHANISMS OF HEAT TRANSFER

• Convection - uses the movement of fluids to transfer heat. • Natural convection (or free convection) refers

to a case where the fluid movement is created by the warm fluid itself.

MECHANISMS OF HEAT TRANSFER

MECHANISMS OF HEAT TRANSFER

• Forced convection uses external means of producing fluid movement. Natural wind and fans are the two most common sources of forced convection.

• Convection coefficient, h, is the measure of how effectively a fluid transfers heat by convection. It is measured in W/m2K, and is determined by factors such as the fluid density, viscosity, and velocity. The rate of heat transfer from a surface by convection is given by:

• where A is the surface area of the object, Tsurface is the surface temperature, and T∞ is the ambient or fluid temperature.

MECHANISMS OF HEAT TRANSFER

• Radiation - does not require a medium for transferring heat; this mode uses the electromagnetic radiation emitted by an object for exchanging heat.

• The amount of radiation emitted by an object is given by:

where: A = surface area, T is the temperature of the body, σ is a constant called Stefan-Boltzmann constant, equal to 5.67×10-8 W/m2K4, and ε is a material property called emissivity.

MECHANISMS OF HEAT TRANSFER

• The emissivity has a value between zero and 1, and is a measure of how efficiently a surface emits radiation. It is the ratio of the radiation emitted by a surface to the radiation emitted by a perfect emitter at the same temperature.

SAMPLE PROBLEMS

1. Calculate the rate at which heat would be lost on a cold January day through a 6.2 m x 3.8 m concrete wall 25 cm thick in Baguio City. The inside temperature is 29 degree Celsius and the outside temperature is 9 degree Celsius. Assume that the thermal conductivity of concrete is 0.8 W/m.

2. A wall of area consists of two slabs, one of thickness and the thermal conductivity and the other one thickness of and thermal conductivity of . The temperature are and . Calculate the thermal conductivity of the wall in terms of the parameters given and if .