1. Heat is a form of energy that gives us the sensation of warmth.
  2. Temperature is the measure of how hot or cold a body is.
  3. Heat is a cause and temperature is an effect.
  4. In this blog, we will discuss heat, heat equation, temperature, specific heat capacity, anomalous expansion of water, and related numerical problems with exercises.

Unit-4 | HEAT | Class-10


Heat:

Heat is a form of energy that gives us the sensation of warmth. All those substances which can produce heat are called the sources of heat. Some sources of heat are the sun, nuclear reaction, chemical reaction, etc.

Remember: Heat always flows from a hotter body to a colder body.

Heat as energy:

We have been learning, "Heat is a form of energy that gives us the sensation of warmth." But, what really makes the heat a form of energy?

Energy is the capacity to do work. Also, if an object or body has the capability to do work, it is said to have energy. We know, we can perform a number of works using heat energy such as cooking food in a stove, running industries via solar energy, melting iron into different shapes, and many more. So, there are a lot of such possibilities where heat can be used to do work. So, it is said to be a form of energy. In fact, the heat energy that is trapped in the Earth's atmosphere makes the Earth a place to live in.

How is heat energy produced? Molecules are contained in a body. If these molecules stay stable and do not move, then the body is felt cold. This is why the body of a dead person is cold. But, when those molecules start vibrating or if they move around then, heat is produced in that body. Therefore, heat energy is the sum total of the kinetic energy contained by the molecules in a body.

The amount of heat contained by a body always depends on the following two factors:
  1. Mass of the body
  2. The average kinetic energy of the molecules
As a relation, the amount of heat energy contained by a body can also be represented as the following:

Amount of heat (Q) ∝ mass of the body (m) × Average K.E. of the molecules


    Unit of Heat:

    Heat is measured in Joule and Calorie. The S.I. unit of heat energy is Joule and the C.G.S. unit of heat energy is Calorie. The substance used to measure heat energy of a body is called calorimeter.


    Relation between Joule and Calorie:

    4.2 J = 1 calorie

    1 calorie Heat is defined as the amount of heat required to raise the temperature of 1 gram pure water by 1°C or 1K. 


     Effects of Heat:

    The effect of heat is well-known to us. The effects of heat are given below:

    It changes the temperature of the body:
    We all know, heat is a cause and temperature is the effect. When we come in contact with a hot object then our body also gets hot and thus, increases the temperature of the body.

    It changes the state of body:
    Here, state of body refers to solid, liquid and gas. When we heat ice (solid), it melts and changes into water (liquid) and when we heat water (liquid) it changes into vapor (gas). Thus, heat can change the state of body.

    It changes the size or volume of the body:
    When we place a balloon inside a hot water then, the molecules inside that balloon start moving rapidly and take more space as a result, the balloon becomes bigger. Hence, the heat can change the size or volume of the body.

    It changes the solubility of the body:
    When we heat the given solvent, then the inter-molecular space between the solutes get broken down by the increase in K.E. of the solvent and more solute can dissolve in that solvent. Hence, it changes the solubility of the body.

    It changes the chemical properties of the body:
    Endothermic reactions require heat to cause the chemical change. Therefore, heat can change the chemical properties of the body.


    Anomalous expansion of water:

    From our general understanding, we have understood that, substances expand on heating and contract on cooling. But, it is somehow different for water at a certain temperature range i.e. 0° to 4°  C.

    When water is heated at 0° to 4°  C, it contracts and when it is cooled at 4°  to 0°C, it expands. But, it shows normal change after 4°  C.

    Definition: The unusual behavior of water between 0°to 4° C is called the anomalous expansion of water. 

    Key point: The water at 4° C has the highest density and the least volume.




    Temperature:

    The measure of how hot or cold a body is, is called temperature. It is the effect of heat . It is the factor which determines the flow of heat.


    Measure of Temperature:

    The device used to measure temperature of  body is called thermometers. The SI unit of temperature is Kelvin (K). 
    Thermometer is based on the principle that, "the substance expands on heating and contracts on cooling." 

    Note: The normal body temperature of human body is 37°C or 98.6°F.


    Temperature Scales:

    There are three temperature scales. They are; Fahrenheit, Celsius and Kelvin. 
    The temperature of pure melting ice at normal atmospheric pressure is called Upper Fixed point. The temperature of pure boiling water at normal atmospheric pressure is called Lower Fixed point.

    The upper fixed point and lower fixed point in every temperature scales are noted below:

    Celsius Scale:
    Lower fixed point: 0°C
    Upper fixed point: 100° C

    Fahrenheit Scale:
    Lower fixed point: 32° F
    Upper fixed point: 212°F.

    Kelvin Scale:
    Lower fixed point: 273° K
    Upper fixed point: 373° K

    Relation between three temperature scales:
    C-0 /100 = F-32/180 = K-273/100


    Heat Equation: 

    Heat equation is an equation that shows how the heat is gained or lost by a body having a mass and change in temperature. 


    Derivation of heat equation:


    Let us suppose that a body of mass(m) has its initial temperature 't1' and amount of heat supplied or taken out from the body is Q. So, that its final temperature becomes 't2', then we have;

    amount of heat gained or lost (Q)  mass of the body(m) and 
    amount of heat gained or lost (Q)  change in temperature (t2-t1) = dt

    'd' refers to the difference in t

    We get,
    Q  m ........(i)
    Q  dt ........(ii)
    Combining equation (i) and (ii), we get,
    Q  mdt
    Therefore, Q = msdt ...... (iii)
    Where s is the proportionality constant known as the specific heat capacity of the substance. 

    The relation given by equation (iii) is called the heat equation.

    Specific heat capacity;

    From the heat equation, we have:
    Q = msdt
    So, s = Q /mdt

    When m= 1 kg and change in temperature (dt) = 1° C or 1° K, then
    s= Q
    Hence,
    specific heat capacity can be defined as the amount of heat gained or lost by a substance of mass 1 kg and to change its temperature by 1° C or 1° K.

    Its SI unit is J/kg° C.

    The substances having more specific heat capacity get heated and cooled slower and substances having less specific heat capacity get heat and cooled faster. Different substances have different heat specific capacity.


    #What do you mean by the statement that the specific heat capacity of water is 4200J/kg° C. 

    Ans: The specific heat capacity of water is 4200 J/kg°C means that 4200J energy is needed to raise the temperature of water through 1° C.


    Principle of calorimeter:

    The principle of calorimeter states that, "The amount of heat lost by a hotter body is equal to the amount of heat gained by a colder body when they are kept in thermal contact."
    i.e. Heat lost = Heat gained

    Making this principle simple, it means that when we bring two bodies in contact with each other, suppose body A is hot and body B is cold in comparison. Then, the transfer of heat energy takes places there. After some time, we can observe that, the temperature of both the bodies become equal which means that, the heat lost by the body A was gained by the body B. Search in the Internet for its experimental verification. 


    #Numerical Problem


    1. Calculate the amount of heat required to change the temperature of an iron ball of mass 3 kg from 30° C to 200°C. (Specific heat capacity of iron is 460 J/kg° C.)
    Solution:
    We have,
    mass(m) = 3kg
    specific heat capacity (s) = 460 J/kg° C
    dt (difference in temperature) = 200° C- 30°C

    Q = msdt 
    = 3 x 460 x (200-30) C
    = 234600 J      

    2. Calculate the final temperature when 2400 joules of heat is given to an iron of mass 2kg at 20°C. (Specific heat capcity = 460 J/kg° C) 

    Solution:
    We have,
    mass(m) = 2kg
    amount of heat gained (Q) = 2400 J
    specific heat capacity = 460 J/kg°C
    t1 = 20°C

    Now,
    Q = msdt
    or, 2400 = 2 x 460 x  (t2 - t1)
    or, 2400 / 920 = t2 - 20
    or, 2.6 +20 = t2
    So, t2 = 22.6° C
    So, the final temperature of the iron in the given condition is 22.6° C.


    3. Hot water at 100°C is added to 300 g of water at 0° C until the final temperature is 40° C. Find the mass of hot water added.

    Solution:
    Given,
    temperature of hot water (t1) = 100°C
    final temperature (t) = 40°C
    Let, mass of hot water be m1

    temperature of cold water (t2) = 0°C
    mass of cold water (m2) = 300g
    = $\dfrac{300}{1000}$kg
    = 0.3 kg

    Now,
    According to the principle of calorimetry,
    m1s1(t1 -t) = m2s2(t -t2)

    [specific heat capacity of water is same]
    So,
    m1(t1- t) = m2(t -t2)
    or, m1(100° -40°) = 0.3(40° -0°)
    or, m1(60°) = 0.3(40°)
    or, m1 = 0.3 $\frac{40°}{60°}$
    or, m1 = 0.3 * $\frac{2}{3}$
    So, m1 = 0.2 kg

    Hence, the mass of the hot water was 0.2 kg.

    4. What is the specific heat capacity of water if 2.1 x 10^5 joule heat is required for 2kg of water to raise its temperature from 40° C to 65° C? 

    Solution:
    Given,

    amount of heat energy (Q) = 2.1*10⁵ J
    mass of water (m) = 2kg
    initial temperature (t1) = 40°C
    final temperature (t2) = 65°C
    difference in temperature (dt) = t2-t1 = 65°C-40°C = 25°C
    Let, specific heat capacity of water be 's'

    Using the heat equation,

    Q = msdt

    or, s = $\dfrac{Q}{mdt}$

    or, s = $\dfrac{2.1*10^5}{2 *25}$

    or, s = $\dfrac{210000}{50}$

    So, s = 4200 J/kg°C

    Hence, the required specific heat capacity of water is 4200 J/kg°C.

    Some more numerical questions for your practice:
    • If 50 kg of heat is supplied to 10kg of water, what is the rise in temperature? (Specific heat capacity of water = 4200 J /kg° C ) (Ans: 1.19°C)

    Practice the heat equation and remember that Q = msdt is the the important equation for every Numerical problem from this chapter.