# heat and calorie

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HeatBy: Kim Reymart Sumayan

Early Theory of Heat; the calorie

Indeed, an 18th century theory of heat pictured heat flow as movement of fluid substance called caloric. According to the caloric theory, any object contained a certain amount of caloric; if more caloric flowed into the object, its temperature increased, and if more caloric flowed out, the objects temperature decreased. When a material was broken apart, such as during burning, a great deal of caloric was believed to be released.

A common unit for heat that is still used today is named after caloric. It is called calorie and is defined as the amount of heat necessary to raise the temperature of 1 gram of water by 1 Celsius degree. More often used than the calorie is the kilocalorie (kcal) which is 1000 calories. Thus, 1 kcal is called a Calorie, and it is with this unit that the energy value of food is specified.

Calories are a measure of energy and can be used to describe any fuel, from petrol to bread. One calorie is the amount of energy required to raise the temperature of one gram (0.035 ounces) of water by one degree Celsius (1.8 degrees Fahrenheit). Food labels often quote energy content in kilocalories (kcal), because food is so rich in energy that it makes more sense to label 1,000 calories at a time. This means a biscuit labelled as having ‘100 Calories’ actually has 100,000 calories, and can raise the temperature of one kilogram (0.45 pounds) of water from freezing to boiling point.

The number of calories in any given item of food is calculated by measuring how much energy is released when a substance is burnt. Inside our bodies, molecular machinery is responsible for burning the fuel we eat, but in the lab, using a spark gives the same result. The traditional method of calorie calculation is to put the food inside a sealed unit known as a bomb calorimeter.

The food is surrounded by an atmosphere of oxygen to ensure it will burn well, and the container is then sealed and surrounded by a known volume of water. A sparks ignites the food inside and allows it to burn until it is reduced to charcoal, releasing all of the energy contained inside. The energy is converted to heat, which in turn raises the temperature of the water. By measuring the water’s temperature change, you can then find out exactly how much energy has been released, and calculate the calories from there.

Heat as Energy Transfer; the Mechanical Equivalent of HeatIt was Benjamin Thompson (1753—

1814), who became acutely aware of this problem when he was supervising the boring of the cannon barrels. Rumford rejected the caloric theory and proposed instead that heat is kind of motion. He claimed that in some circumstances, at least, heat is produced by doing mechanical work.

James Prescott Joules (1818—1889) performed a number of experiments that were crucial in establishing our present-day view that heat, like work, represents a transfer of energy. Joule found that a given amount of work was always equivalent to a particular amount of heat. This is known as mechanical equivalent of heat: 4.186 J = 1 cal 4.186 x 103 = 1 kcalThus, heat is an energy that is transferred from one body to another because of a difference in temperature.

However, a second definition is often used:1 cal = 4.184 J;This is called the thermochemical calorie.

Distinction Between Temperature, Heat, and Internal

EnergyThermal Energy, or Internal Energy is the sum total of all the energy of all the molecules in an object.Heat is not the energy a body contains but rather refers to the amount of energy transferred from a hot to a cold body.Temperature is a measure of the average kinetic energy of individual molecules.

For example, if a 50 gram of water at 30o C is placed in mixed with 200 grams of water at 25o C, heat flows from the water at 30o C to the water at 25o C even though the internal energy of the 25o C water is much greater because there is much more of it.

Internal Energy of an Ideal GasThe internal energy, U, is the sum of the translational kinetic energies of all atoms. This sum is just equal to the average kinetic energy per molecule times the total number of molecules, N: U = N (1/2 mv2 ) U = 3/2 NkT U = 3/2 nRT Where n is the number of moles.Thus, the internal energy of an ideal gas depends only on the temperature and the number of moles of gas.

Also, if the molecules contain one or more atoms, then the rotational and vibrational energy of the molecules must be taken into account. This also include the pressure and volume, But for liquids and solid, includes electrical potential energy associated with the forces between atoms.

Specific HeatThe amount of heat Q required to change the temperature of a system is found to be proportional to the mass m of a system and to the temperature change T, is expressed in the equation, Q = mc TWhere c is a quantity characteristic of the material called specific heat. For water at 15o C and a constant pressure of 1atm, c = 1.00 kcal/kg*C, or 4.18 x 103 J/kg*C, since by definition, it takes 1 kcal of heat to raise the temperature of 1kg of water by 1o C

Specific Heat ( 20 C and constant pressure of 1 atm)

Substance specific heat, cp

kcal/kg*C J/kg*C

Aluminum 0,22 900 Copper 0.093 390 Glass 0.20 840 Ice (-5 oC) 0.50 2100 Lead 0.031 130 Human Body (average) 0.83 3470 Water (15o C) 1.00 4186

Example No. 1 How much heat is required to raise the temperature of 20kg of iron from 10o C to 90 degree Celsius? (For god sake, pls answer it on the board!) Example No.2 If 200 cubic centimeter of tea at 95 degrees Celsius is poured into a 300g glass cup initially at 25 degrees Celsius, what will be the final temperature of the mixture when equilibrium is reached, assuming that no heat flows out.

Latent Heat (l)

The heat required to change 1.0 kg of substance to change from the solid to a liquid state is called heat of fusion, and denoted by lf and the heat fusion of the water is 79.7 kcal/kg .

The heat required to change a substance from liquid to vapor phase is called the heat of vaporization, lv and for the water it is 539 kcal/kg

The values for heat of fusion and vaporization are also called latent heats. (On the table)

The heat involve in a change of phase depends not only on the latent heat but also on the total mass of the substance.

Q = ml ;m, mass and l for the latent heat of a specific substance.Ex.When a 5.00 kg of water freezes at 0 degrees Celsius, the heat release would be, 5.00 kg x 79.7 kcal/kg = 398 kcal heat will be released( Further example at the board)

Heat Transfer

A. Conduction B. Convection C. Radiation

A. Conduction Conduction is when we put a silver spoon on a hot

cup of coffee and the result is the exposed end becomes to hot even though it is not directly in contact with the heat. Heat conduction can be visualize as the result of molecular collision. At a molecular level, the heated part of a spoon molecules will vibrate faster and faster and they will collide the neighboring molecules and the slow moving molecules will then gain energy and it will start to move faster and faster, then in turn will transfer some of their energy by collision of molecules still further down the object.

Indeed it is found experimentally that the rate of a heat flow through the substance is proportional to the difference in temperature between its ends. It also depends on the size and shape of an object. It is found experimentally that the heat flow per time interval is given by the relation Q/ t =kA T2 – T1/ l ( please refer to the board for further clarification) where A is the cross-sectional area of the object,

l is the distance between two ends, which are temperatures T1 and T2 ,and the k is a proportionality constant called the thermal conductivity, which is the characteristic of the material. (Examples on the board) ( Thermal conductivities k on the table at the board)Mentionables: Conductors Insulators

B. Convection

It is a process whereby heat is transferred by the mass movement of molecules from one place to another.

Example is the fan, the warm or cold air in the pacific ocean, water in a pot being boiled.

C. RadiationIf convection and conduction requires the present of matter. The radiation does not, it consist essentially of electromagnetic waves which include the IR that is responsible for heating the Earth.

The rate at which an object radiates energy has been found to be proportional to the fourth power of the Kelvin temperature. That is a body at 2000 K as compared to one at 1000 K radiates energy at a rate of 24 = 16 times as much. The rate of radiation is also proportional to the area A of the emitting object so the rate at which energy leaves the object, Q/ t, is (pls refer to the board)

e, is called the emissivity, and is a number between 0 and 1 that is the characteristic of a material, such as a charcoal, have emissivity close to 1 because of black surface, while shiny surface is close to zero thus emit correspondingly less radiation. ( Please refer to the board)

By:Kim Reymart Sumayan

Thank You for Listening!!!

Credits:Kim Reymart Sumayan