Rate in Thermal Systems Overview Rate in Thermal Systems 1
Fundamental Concepts What is the prime mover in the thermal system? temperature difference ( T) What does rate measure in the thermal system? heat flow (Q H ) How does heat flow? from areas of high temp to low temp Rate in Thermal Systems 2
Heat Flow Why does heat flow? molecules with high temperature vibrate faster than molecules at lower temperature more kinetic energy when the molecules bump into one another, energy is transferred from the high energy molecule to the low energy molecule this continues until all the molecules have equal energy levels Rate in Thermal Systems 3
Heat vs Temperature? What is heat? Heat is a form of energy relating to the vibrating motion of atoms and molecules What is temperature? Temperature is a measure of the average kinetic energy of the molecules of a substance Rate in Thermal Systems 4
Calculation of Heat Flow (Q H ) How do we calculate heat flow? Heat Flow = Heat energy transferred/elapsed time Quantity of heat = amount of heat energy moved per unit time Q H = H/t Rate in Thermal Systems 5
Units of Heat Flow - Metric What are the units for heat flow? any unit of heat / any unit of time common units J/s; cal/s; Btu/hr What is a calorie? amount of heat required to raise the temperature of one gram of water one degree Celsius; Often a kilocalorie = 1000 cal is used SI (metric) unit of heat flow Rate in Thermal Systems 6
Units of Heat Flow - British What is a Btu? British thermal unit amount of heat required to raise the temperature of one pound of water one degree Fahrenheit Rate in Thermal Systems 7
Specific Heat What is specific heat? every substance has a unique specific heat it is a fixed quantity and is the amount of heat required to raise one gram of a specific substance by one degree Celsius used to determine the amount of heat required to change the temperature of a mass of a substance Symbol is c Rate in Thermal Systems 8
Calculation of Heat Energy What is the equation for calculating heat energy during a temperature change? H = (m)(c)( T), where H = amount of heat m = mass of sample c = specific heat of substance, and T = Final temp initial temp Rate in Thermal Systems 9
Example - Specific Heat Calculations What is the specific heat of water? 1 cal/gm- o C or 1 Btu/lb- o F Example How much heat is required to heat 417 pounds of water from 70 o F to 130 o F? H = (m)(c)( T) H = (417 lbs)(1 Btu/lb- o F)(130-70) H = (417)(1)(60) H = 25,020 Btu Rate in Thermal Systems 10
Heat Exchange - Hot to Cold Suppose you heat a metal ball and place it in a cup of cold water. How does the heat flow? heat will flow from the ball to the water the amount of heat lost by the metal is equal to the amount of heat gained by the water This is an example of conservation of energy Rate in Thermal Systems 11
Example of Heat Exchange Example A 25kg brass ball at 100C is placed in a container of water at 10C. When the brass-water system has stabilized the final temperature is 30C. How much heat (H) was removed from the brass ball and added to the water? (c for brass = 0.091 kcal/c ) What is the mass of water in the container? Rate in Thermal Systems 12
Calculations of Heat Transfer Part 1 H = mc T H = 25 (0.091)(100-30) H = 159.3 kcal = 159,300 cals Part 2 heat lost by ball was added to water H = mc T 159,300 = m(1)(30-10) 159,300 = 20m m = 159300/20 m = 7965 gm Rate in Thermal Systems 13
Heat Flow Rating An air conditioner is rated at 10,000 Btu. What does this mean? The unit can remove heat at a rate of 10,000 Btu per hour This removal of heat will cause a change in temperature Rate in Thermal Systems 14
Calculation of Heat Flow Rating Example A 5000 Btu heater runs for 5 hours and 30 minutes. How much (what quantity of) heat is moved? Q H = H/t 5000 Btu/hr = H/5.5 hrs H = 27,500 Btu Rate in Thermal Systems 15
Heat flow Rate & Thermal Conductivity What factors affect the heat flow rate (Q H ) across a material of thickness (l), temp difference ( T), area (A) and thermal conductivity (k)? Q H = ka T/l, where Q H is measured in units such as Btu/hr, or cal/sec Rate in Thermal Systems 16
Thermal Conductivity Examples Examples of thermal conductivity, in British units, are: Air = 5.7 x 10-4 Corkboard = 0.30 Aluminum = 1400
Heat Amount vs Heat Flow Rate H = The amount of heat that can be added to or removed from a body Q H = the rate of heat flow through a material due to a temperature difference across the material, for example: Inner and outer walls on a house, ski jacket, etc Rate in Thermal Systems 18
Change of State What is a change of state? changing a substance from a solid to a liquid or a gas Solid-liquid = melt Liquid-gas = vaporize Rate in Thermal Systems 19
Types of Heat What is sensible heat? Applied heat that changes the temperature of a substance What is latent heat? Applied heat that does not change the temperature of a substance the applied heat causes the substance to change state (from a solid to liquid) Rate in Thermal Systems 20
Latent Heat Schematic Rate in Thermal Systems 21
Rate in the Thermal System Example A sample of ice at -10 o C is heated until it becomes steam at 110 o C. Classify the heat changes as latent or sensible. -10 o C ice to 0 o C ice sensible 0 o C ice to 0 o C water latent 0 o C water to 100 o C water sensible 100 o C water to 100 o C steam latent 100 o C steam to 110 o C steam sensible Rate in Thermal Systems 22
Temperature measuring devices Thermometers Celsius (C) Fahrenheit (F) Thermocouples The temperature of the junction of 2 different metals translates to voltage Rate in Thermal Systems 23