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# Heat and Temperature

• Last Updated : 16 Jun, 2021

Heat describes the thermal phenomena, we shall primarily describe two physical quantities called heat and temperature. Heat is a form of energy and can be expressed in energy units defined in mechanics. But the temperature can not be defined in terms of the three fundamental quantities viz., length, mass, time. Thus, the temperature is a new fundamental quantity of a type different from the above fundamental quantities.

Starting from the discovery of a thermometer by Galileo at the end of the 16th century, the long history of thermometry and the establishment of the concept of temperature is an interesting story of its own; but we may simply understand the temperature to be the scale reading of a suitable thermometer placed in close contact with the object. Temperature is used to measure the coldness or hotness of the body.

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### Heat

Heat is perceptible only when it passes from one body to another. As a result of heat communication, the temperature of the recipient increases and the temperature of the donor decreases. Thus, the quantity of heat that a substance either releases or receives can only be measured.

Heat is a form of energy that is transferred between two bodies because of a temperature difference existing between them.

In principle, heat gained or lost by a substance is measured by the calorimetric principle. The unit of heat called the gram-calorie or simply calorie is the quantity of heat required to raise the temperature of 1 gm of water by 1 °C. Other units of heat are set listed below.

Units of Heat:

Calorie: One calorie is the quantity of heat that must be given to 1g of water to raise its temperature by 1°C.

Kilogram Calorie: One-kilogram calorie is equal to 1000 calorie ie, it is the quantify of heat which must be given to 1000 g of water to raise its temperature by 1°C

Specific heat: It is the ratio of the quantity of heat required to raise the temperature of a unit mass of the substance through a certain range of temperature to the quantity of heat required to use the temperature of the unit mass of water through the same range of temperature.

Specific heat=(Heat required to raise the unit mass of a substance by 1°)/(Heat required to raise the unit mass of water by 1°)

Specific heat is different for different substances.

Unit: C.G.S= “calorie/g°C”  , S.I= “Joule/kg. Kelvin”

Amount of heat absorbed or given out by a body for rising or fall of temperature.

Heat= mass×specific heat×temperature change

Thermal capacity: The thermal capacity of a substance is the quantity of heat required to raise its temperature by 1°.

Thermal capacity of a substance= Mass of substance×Specific Heat.

Specific Heat=(Thermal capacity of a substance)/(Mass of substance)

Unit:  C.G.S= “calorie/°C”  , S.I= “Joule/Kelvin” or “Joule/°C”

Water equivalent: The water equivalent of a body is defined as the mass of water that will be heated through 1° by the amount of heat that raises the temperature of the body itself by 1°.

Water equivalent of the body, W= ms g

It is obvious that the expression for heat lost or gained by a body can be written as Q=Wt

Heat gained or lost = Water equivalent of the body×rise or fall in temperature.

Temperature

Temperature is a measure of the degree of hotness or is the intensity of sensible heat. Whenever two bodies at different temperatures are brought into thermal contact, heat flows from one at a higher temperature to the other at a lower temperature.

Temperature: Temperature may be defined as the thermal condition of a body that determines the direction of heat flow i.e., it determines whether the body will receive heat from another body or it will give heat to the same.

The human body is quite sensitive to changes in temperature. But the sense of touch is purely qualitative. while scientific experiment requires that every physical quantity should be measurable. Instruments which is used to measurement of temperature are called thermometers.

Difference between heat and temperature:

Thermal equilibrium:

When a hot body is brought into thermal contact with a cold body, the hot body loses heat and the cold body gains the same amount of heat. After some time both reach an intermediate temperature. The flow of heat then ceases and the bodies are then said to be at thermal equilibrium.  Similarly, When two gas, one hotter and the other colder, are brought a thermal contact, then when heat exchange continues the properties like pressure or volume or both change. However, when thermal equilibrium is reached, then no further change in these properties occur.

Zeroth law of thermodynamics:

Let us consider two systems P and Q. They are separated from each other by an insulating wall so that no heat exchange takes place between them. Each of these two systems is brought into thermal contact with a third system D through conducting walls. All these systems are surrounded by an insulating wall so that no heat exchange with the surroundings is possible. Experiments show that the exchange of heat takes place between P and Q  and D till both P and Q reach thermal equilibrium with D with appropriate changes in their properties. If the insulating wall between P and Q is now replaced by a conducting wall, then it will be observed that no further changes in properties of P and Q occur. These experimental facts are expressed in the form of a law known as the zeroth law of thermodynamics

The law states that Two systems in thermal equilibrium with a third are in thermal equilibrium with each other.

This law enunciated by Fowler has formulated after the first and the second laws of thermodynamics hence the name Zeroth law of thermodynamics.

Concept of temperature: This law immediately leads us to the concept of temperature. A number of systems in thermal equilibrium with one another must possess a common value of some property, So if. this property is the same for some systems, then they will be in thermal equilibrium and if not, then there will be an exchange of thermal energy among them till this property is the same for all of them when they reach thermal equilibrium with one another. This property is called temperature.

Temperature:The temperature of a system is defined as that property that determines whether or not the system is in thermal equilibrium with other systems.

Question 1:  If a mercury thermometer is held in a flame, then the column of mercury at first goes down and then rises. Why?

If a mercury thermometer is held in a flame, then by absorbing heat its glass bulb expands first. Glass is a bad conductor of heat; so heat is not conducted to mercury instantaneously. The column of mercury at first goes down due to this reason. But after a short interval, mercury absorbs heat and expands; then the column rises.

Question 2:  Is the solar system in thermal equilibrium?

Because the temperatures of the sun and the planets and the satellites are all different. So the solar system is not thermal equilibrium.

Question 3: The temperature of a room is 25°C. Some people enter the room. Will thermal equilibrium be established after some time?

The normal temperature of a human is 37°C.  But the temperature of the room is lower than the human temperature (25°C). So thermal equilibrium will not be established.

Question 4: Calculate what should be the thermal capacity and water equivalent of 10g of aluminium of specific hear 0.21. How much heat would be necessary to raise the temperature from 0°C to 30°C?

Mass=10g,  Specific heat=0.21

Thennal capacity of 10 g of aluminium = 10×0.21 Cal/°C

water equivalent of 10 gm of aluminium=2.1g

The heat required to raise the temperature of 10g aluminium from 0°C to 30°C= 2.1×30 cal = 63 Cal.

Question 5: Application of Zeroth law of thermodynamics.

• Hot tea becomes cold after some time.
• The thermostat.
• The vegetable is cool down when kept in the refrigerator.
• Measuring the temperature of the body using a thermometer.
• Temperature measurement of Air condition.

Question 6: The ratio of the densities of the two materials are 2∶3 and their specific heats are 0.12 and 0.09 respectively. Determine the ratio of their thermal capacities per unit volume.

Answer:As mass(m) =volume ×density(ρ), so for unit volume of material, mass=density(ρ).

(Thermal capacity per unit volume of the first/Thermal capacity per unit volume of the second)=(ρ1s12s2)

=(2×0.12/3×0.09)

=(8/9)

Question 7: 100g of copper are heated to 100°C and put into 150 g of an oil (sp. heat 0.51) at 10°C, contained in a copper calorimeter weighing 40 g. The temperature rises to 19.5°C. Find the specific heat of copper.

Let s be the required sp. heat of copper.

Heat given out by copper= 100×s×(100-19.5) Cal = 8050s Cal.

Heat gained by the oil= 150×0.51×(19.5-10) Cal= 726.75 Cal.

Heat gained by the calorimeter =40×s×(19.5-10) Cal = 380s Cal.

Heat gained= Heat lost.

726.75+380s=8050s

7670s=726.75

s=0.095

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