Is The Temperature Increasing Or Decreasing At The Point In The Direction Of

Rates of Heat Transfer

On previous pages of this lesson, nosotros take learned that heat is a form of energy transfer from a high temperature location to a low temperature location. The 3 main methods of heat transfer - conduction, convection and radiation - were discussed in particular on the previous folio. Now we will investigate the topic of the rate of heat transfer. This topic is of peachy importance because of the frequent need to either increase or decrease the rate at which heat flows between two locations. For instance, those of us who live in colder winter climates are in constant pursuit of methods of keeping our homes warm without spending besides much money. Heat escapes from higher temperature homes to the lower temperature outdoors through walls, ceilings, windows and doors. Nosotros make efforts to reduce this heat loss by adding amend insulation to walls and attics, caulking windows and doors, and buying high efficiency windows and doors. As another case, consider electricity generation. Household electricity is nigh oftentimes manufactured by using fossil fuels or nuclear fuels. The method involves generating heat in a reactor. The heat is transferred to water and the water carries the heat to a steam turbine (or other type of electric generator) where the electricity is produced. The challenge is to efficiently transfer the oestrus to the water and to the steam turbine with as little loss equally possible. Attention must be given to increasing heat transfer rates in the reactor and in the turbine and decreasing heat transfer rates in the pipes between the reactor and the turbine.

So what variables would affect the oestrus transfer rates? How can the rate of heat transfer exist controlled? These are the questions to be discussed on this page of Lesson 1. Our discussion will be restricted to the variables affecting the rate of heat transfer by

conduction

. Once the variables affecting the charge per unit of heat transfer are discussed, we will look at a mathematical equation that expresses the dependence of rate upon these variables.

Temperature Difference

In conduction, oestrus is transferred from a hot temperature location to a cold temperature location. The transfer of heat will continue every bit long equally there is a departure in temperature betwixt the two locations. Once the two locations have reached the aforementioned temperature, thermal equilibrium is established and the oestrus transfer stops. Earlier in this lesson, we discussed the transfer of heat for a situation involving a metal can containing high temperature water that was placed within a Styrofoam cup containing low temperature water. If the two water samples are equipped with temperature probes that record changes in temperature with respect to fourth dimension, then the following graphs are produced.

In the graphs above, the slope of the line represents the rate at which the temperature of each individual sample of h2o is changing. The temperature is changing because of the heat transfer from the hot to the cold h2o. The hot h2o is losing energy, so its slope is negative. The cold h2o is gaining energy, so its slope is positive. The rate at which temperature changes is proportional to the rate at which estrus is transferred. The temperature of a sample changes more rapidly if heat is transferred at a loftier charge per unit and less rapidly if heat is transferred at a low rate. When the two samples reach thermal equilibrium, there is no more heat transfer and the slope is zero. So we can think of the slopes as beingness a measure of the charge per unit of heat transfer. Over the course of time, the rate of heat transfer is decreasing. Initially heat is being transferred at a high rate as reflected past the steeper slopes. And every bit time progresses, the slopes of the lines are condign less steep and more than gently sloped.

What variable contributes to this subtract in the heat transfer charge per unit over the course of time? Answer: the deviation in temperature between the two containers of h2o. Initially, when the charge per unit of rut transfer is high, the hot h2o has a temperature of 70°C and the cold water has a temperature of v°C. The ii containers accept a 65°C difference in temperature. As the hot water begins to cool and the cold water begins to warm, the departure in their temperatures decrease and the rate of heat transfer decreases. Equally thermal equilibrium is approached, their temperatures are approaching the aforementioned value. With the temperature difference approaching zero, the rate of heat transfer approaches cipher. In conclusion, the rate of conductive heat transfer between two locations is afflicted by the temperature departure between the two locations.

Material

The kickoff variable that we have identified every bit affecting the rate of conductive heat transfer is the temperature difference between the two locations. The 2nd variable of importance is the materials involved in the transfer. In the previous discussed scenario, a metal can containing high temperature water was placed within a Styrofoam cup containing depression temperature water. The heat was transferred from water through the metallic to water. The materials of importance were h2o, metal and h2o. What would happen if the oestrus were transferred from hot water through glass to cold h2o? What would happen if the oestrus were transferred from hot h2o through Styrofoam to cold water? Answer: the charge per unit of estrus transfer would be different. Replacing the inner metallic tin can with a glass jar or a Styrofoam cup would change the rate of rut transfer. The charge per unit of heat transfer depends on the material through which heat is transferred.

The effect of a material upon heat transfer rates is often expressed in terms of a number known equally the thermal electrical conductivity. Thermal conductivity values are numerical values that are determined by experiment. The higher that the value is for a particular cloth, the more chop-chop that heat volition be transferred through that material. Materials with relatively high thermal conductivities are referred to every bit thermal conductors. Materials with relatively depression thermal conductivity values are referred to as thermal insulators. The tabular array below lists thermal conductivity values (k) for a diversity of materials, in units of W/m/°C.

Material	k	Cloth	k
Aluminum (s)	237	Sand (due south)	0.06
Contumely (south)	110	Cellulose (s)	0.039
Copper (s)	398	Glass wool (s)	0.040
Gold (s)	315	Cotton wool (s)	0.029
Cast Iron (due south)	55	Sheep's wool (south)	0.038
Lead (south)	35.2	Cellulose (s)	0.039
Silver (south)	427	Expanded Polystyrene (s)	0.03
Zinc (s)	113	Wood (s)	0.13
Polyethylene (HDPE) (s)	0.5	Acetone (fifty)	0.16
Polyvinyl chloride (PVC) (southward)	0.19	H2o (l)	0.58
Dense Brick (s)	1.6	Air (g)	0.024
Concrete (Depression Density) (southward)	0.2	Argon (g)	0.016
Physical (High Density) (s)	1.v	Helium (thousand)	0.142
Ice (s)	2.xviii	Oxygen (k)	0.024
Porcelain (s)	1.05	Nitrogen (m)	0.024

Source: http://world wide web.roymech.co.uk/Related/Thermos/Thermos_HeatTransfer.html

Equally is apparent from the tabular array, estrus is generally transferred by conduction at considerably college rates through solids (s) in comparing to liquids (l) and gases (g). Heat transfer occurs at the highest rates for metals (first 8 items in left-hand column) because the mechanism of conduction includes mobile electrons (every bit discussed on a previous folio). Several of the solids in the correct-hand cavalcade have very low thermal conductivity values and are considered insulators. The structure of these solids is characterized past pockets of trapped air interspersed between fibers of the solid. Since air is a great insulator, the pockets of air interspersed between these solid fibers gives these solids low thermal conductivity values. One of these solid insulators is expanded polystyrene, the textile used in Styrofoam products. Such Styrofoam products are made by blowing an inert gas at high pressure into the polystyrene earlier being injected into the mold. The gas causes the polystyrene to expand, leaving air filled pockets that contribute to the insulating ability of the finished production. Styrofoam is used in coolers, popular tin can insulators, thermos jugs, and even foam boards for household insulation. Another solid insulator is cellulose. Cellulose insulation is used to insulate attics and walls in homes. It insulates homes from rut loss every bit well equally sound penetration. Information technology is oft diddled into attics as loose fill cellulose insulation. It is likewise practical equally fiberglass batts (long sheets of paper backed insulation) to fill the spacing betwixt 2x4 studs of the exterior (and sometimes interior) walls of homes.

Surface area

Some other variable that affects the charge per unit of conductive heat transfer is the surface area through which heat is existence transferred. For case, rut transfer through windows of homes is dependent upon the size of the window. More heat will be lost from a home through a larger window than through a smaller window of the same composition and thickness. More heat volition be lost from a home through a larger roof than through a smaller roof with the same insulation characteristics. Each individual particle on the surface of an object is involved in the heat conduction process. An object with a wider area has more surface particles working to conduct heat. Equally such, the rate of heat transfer is directly proportional to the surface area through which the heat is being conducted.

Thickness or Distance

A final variable that affects the rate of conductive rut transfer is the distance that the heat must be conducted. Oestrus escaping through a Styrofoam cup will escape more rapidly through a thin-walled loving cup than through a thick-walled cup. The rate of rut transfer is inversely proportional to the thickness of the loving cup. A similar statement tin be fabricated for estrus beingness conducted through a layer of cellulose insulation in the wall of a domicile. The thicker that the insulation is, the lower the rate of heat transfer. Those of us who live in colder wintertime climates know this principle quite well. We are told to dress in layers earlier going exterior. This increases the thickness of the materials through which rut is transferred, as well every bit trapping pockets of air (with high insulation ability) between the private layers.

A Mathematical Equation

So far we have learned of four variables that affect the rate of heat transfer between ii locations. The variables are the temperature difference between the 2 locations, the material present between the two locations, the area through which the heat will be transferred, and the distance information technology must be transferred. As is often the case in physics, the mathematical relationship between these variables and the charge per unit of heat transfer tin be expressed in the grade of an equation. Let'southward consider the transfer of heat through a glass window from the inside of a dwelling house with a temperature of T₁ to the outside of a home with a temperature of T₂ . The window has a area A and a thickness d. The thermal conductivity value of the window glass is k. The equation relating the heat transfer charge per unit to these variables is

Charge per unit = k•A•(T₁ - T₂)/d

The units on the rate of estrus transfer are Joule/second, also known as a Watt. This equation is applicable to whatever situation in which heat is transferred in the same direction across a flat rectangular wall. Information technology applies to conduction through windows, flat walls, slopes roofs (without any curvature), etc. A slightly different equation applies to conduction through curved walls such as the walls of cans, cups, glasses and pipes. Nosotros will not hash out that equation here.

Example Problem

To illustrate the use of the above equation, let's calculate the rate of heat transfer on a cold day through a rectangular window that is i.two g wide and 1.8 m high, has a thickness of six.2 mm, a thermal conductivity value of 0.27 Westward/g/°C. The temperature inside the dwelling is 21°C and the temperature outside the abode is -4°C.

To solve this problem, we will demand to know the surface expanse of the window. Being a rectangle, we tin calculate the area as width • pinnacle.

Area = (1.2 m)•(1.eight yard) = 2.sixteen chiliad^two.

We volition besides need to give attending to the unit on thickness (d). It is given in units of cm; we will need to catechumen to units of meters in social club for the units to be consistent with that of k and A.

d = 6.two mm = 0.0062 m

At present we are set up to summate the rate of heat transfer past substitution of known values into the above equation.

Charge per unit = (0.27 W/m/°C)•(ii.xvi m²)•(21°C - -4°C)/(0.0062 k)
Rate = 2400 W (rounded from 2352 W)

It is useful to note that the thermal conductivity value of a house window is much lower than the thermal conductivity value of glass itself. The thermal conductivity of glass is nearly 0.96 Westward/m/°C. Glass windows are constructed equally double and triple pane windows with a depression pressure inert gas layer between the panes. Furthermore, coatings are placed on the windows to improve efficiency. The result is that there are a series of substances through which rut must consecutively pass in order to be transferred out of (or into) the house. Like electrical resistors placed in series, a serial of thermal insulators has an additive effect on the overall resistance offered to the flow of oestrus. The accumulative effect of the diverse layers of materials in a window leads to an overall electrical conductivity that is much less than a single pane of uncoated drinking glass.

Lesson 1 of this Thermal Physics affiliate has focused on the meaning of temperature and heat. Accent has been given to the evolution of a particle model of materials that is capable of explaining the macroscopic observations. Efforts take been made to develop solid conceptual understandings of the topic in the absence of mathematical formulas. This solid conceptual understanding volition serve you well as you arroyo Lesson 2. The chapter will turn slightly more mathematical as we investigate the question: how can the amount of heat released from or gained past a system be measured? Lesson 2 volition pertain to the science of calorimetry.

Bank check Your Understanding

one. Predict the effect of the following variations upon the rate at which heat is transferred through a rectangular object by filling in the blanks.

a. If the expanse through which oestrus is transferred is increased by a factor of two, and then the rate of heat transfer is ________________ (increased, decreased) by a cistron of _________ (number).

b. If the thickness of the textile through which heat is transferred is increased by a cistron of 2, so the rate of oestrus transfer is ________________ by a factor of _________.

c. If the thickness of the material through which heat is transferred is decreased by a factor of iii, then the rate of heat transfer is ________________ past a factor of _________.

d. If the thermal conductivity of the material through which heat is transferred is increased by a factor of v, and then the rate of rut transfer is ________________ by a factor of _________.

e. If the thermal conductivity of the material through which estrus is transferred is decreased by a cistron of 10, and then the rate of oestrus transfer is ________________ by a factor of _________.

f. If the temperature difference on reverse sides of the material through which heat is transferred is increased past a factor of ii, then the rate of heat transfer is ________________ by a cistron of _________.

2. Apply the information on this folio to explicate why the two-iv inch thick layer of blubber on a polar carry helps to keep polar bears warm during frigid artic weather.

iii. Consider the example problem above. Suppose that the area where the window is located is replaced past a wall with thick insulation. The thermal conductivity of the same area will be decreased to 0.0039 W/k/°C and the thickness will be increased to xvi cm. Decide the rate of heat transfer through this area of 2.16 grand^two.