3. Thermal Physics

I. Choose the correct answer

1.The value of universal gas constant ______.

(a) 3.81 mol-1 KJ-1
 (b) 8.03 J mol-1 K-1
 (c) 1.38 mol-1 KJ-1
(d) 8.31 J mol-1 K-1.


2.If a substance is heated or cooled, the change in mass of that substance is _____.

(a) positive
 (b) negative
(c) zero
(d) none of the above.

3.If a substance is heated or cooled, the linear expansion occurs along the axis of:

(a) X or -X
(b) Y or -Y
 (c) both (a) and (b)
 (d) (a) or (b)

4. Temperature is the average _____ of the molecules of a substance?

(a) the difference in K.E and P.E.
 (b) the sum of P.E and K.E.
(c) the difference in T.E and P.E.
(d) the difference in K.E and T.E.

5. In the Given diagram, the possible direction of heat energy transformation is _____.

             

II. Fill in the blanks
1.The value of Avogadro number _____.(6.023 × 1023 / mol.)

2.The temperature and heat are _______ quantities.(Scalar)

3.One calorie is the amount of heat energy required to raise the temperature of _____ of water through _________(1 gram,     1°C)

4.According to Boyle’s law, the shape of the graph between pressure and reciprocal of the volume is ________(Straight line)

III. State whether the following statements are true or false. if false explain why?

1.For a given heat in liquid, the apparent expansion is more than that of real expansion.
Answer:  False.
Correct Statement: When the liquid is heated in a container, first heat is gained by container which expands and level of liquid goes down, but immediately liquid receives the heat from container so apparent expansion is liquid.

Real expansion = Expansion of container + Apparent expansion

2.Thermal energy always flows from a system at a higher temperature to a system at a lower temperature.
Answer:           True.

3.According to Charles’s law, at constant pressure, the temperature is inversely proportional to volume.
Answer:           False.
Correct Statement: According to Charle’s law at constant pressure (P), the volume of gas is directly proportional to absolute temperature.
V ∝ T
(or)
T ∝ V.

IV. Match the items in column-I to the items in column-II

Column-I

Column-II

1. Linear expansion

(d) change in length

2. Superficial expansion

(e) change in an area

3. Cubical expansion

(a) change in volume

4. Heat transformation

(b) hot body to cold body

5. Boltzmann constant

(c) 1.381 × 10-23 JK-1


V. Assertion and Reason Type Questions

(a) Both the assertion and the reason are true and the reason is the correct explanation of the assertion.
(b) Both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
(c) Assertion is true but the reason is false.
(d) Assertion is false but the reason is true.

1.Assertion: There are no effects on other ends when the end of the rod is only heated.
Reason: Heat always flows from a region of lower temperature to higher temperature of the rod.
Answer:
(c) The assertion is true but the reason is false.
Correct Reason: Heat always flows from a region of higher temperature to lower the temperature of the rod.

2.Assertion: Gas is highly compressible than solid and liquid
Reason: Interatomic or intermolecular distance in the gas is comparably high.
Answer:
(a) Both the assertion and the reason are true and the reason is the correct explanation of the assertion.

VI. Answer in Briefly

1. Define one calorie.
Answer:
One calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water through 1°C.

2. Distinguish between linear, cubical and superficial expansion.
Answer:

Linear expansion

Cubical expansion

Superficial expansion

When a body is heated or cooled, the length of the body changes due to change in its temperature.

If there is an increase in the volume of a solid body due to heating, it is called as cubical expansion.

If there is an increase in the area of a solid object due to heating, then the expansion is called superficial expansion.

The ratio of increase in the length of the body per degree rise in temperature to its unit length.

The ratio of increase in the volume of the body per degree rise in temperature to its unit volume is called a coefficient of cubical expansion.

The ratio of increase in the area of the body per degree rise in temperature to its unit area is called a coefficient of superficial expansion.

3. What is co-efficient of cubical expansion?

    The ratio of increase in volume of the body per degree rise in temperature to its unit volume is called as coefficient of cubical expansion. This is also measured in K-1.

4. State Boyle’s law.

    When the temperature of a gas is kept constant, the volume of a fixed mass of gas is inversely proportional to its pressure.

5.State-the law of volume.

    According to this law, When the pressure of gas is kept constant, the volume of a gas is directly proportional to the temperature of the gas.

                V ∝ T
                    (OR)
                = constant

6.Distinguish between ideal gas and real gas.

Ideal Gas

Real Gas

If the atoms or molecules of gas do not interact with each other then it is called as an ideal or perfect gas.

If the atoms or molecules of a gases interact with each other with a definite amount of intermolecular (or) interatomic force, then it is called as real gas.

At very high temperature (or) low pressure, a real gas behaves as an ideal gas, because there is no interatomic (or) Intermolecular force of attraction.

At very high temperature (or) low pressure, the interatomic (or) Intermolecular forces of attraction are weak in an ideal gas.

7. What is the co – efficient of real expansion?

    Coefficient of real expansion is defined as the ratio of the true rise in the volume of the liquid per degree rise in temperature to its unit volume.

The SI unit of coefficient of real expansion is K-1.

8. What is co-efficient of apparent expansion?

    Coefficient of apparent expansion is defined as the ratio of the apparent rise in the volume of the liquid per degree rise in temperature to its unit volume. The SI unit of coefficient of apparent expansion is K-1.

VII. Numerical Problems

1. Find the final temperature of a copper rod. Whose area of cross-section changes from 10 m2 to 11 m2 due to heating. The copper rod is initially kept at 90 K. (Coefficient of superficial expansion is 0.0021 K)?
Solution:

2. Calculate the coefficient of cubical expansion of a zinc bar. Whose volume is increased 0. 25 m3 from 0.3 m3 due to the change in its temperature of 50 K?
Solution:
Given: αv of Zn bar
Volume of zinc bar V0 = V1 = 0.3 m3
Change in volume ∆V = V2 – V1 = 0.25 – 0.30 = 0.05 m3
Change in temperature ∆T = 50K
Coefficient of cubical expansion αv = ?

VIII. Answer in Detail

1. Derive the ideal gas equation.
Answer:
The ideal gas equation is an equation, which relates all the properties of an ideal gas. An ideal gas obeys Boyle’s law and Charles’ law and Avogadro’s law.
According to Boyle’s law,
PV = constant ………..…. (1)
According to Charles’s law,
= constant ………………. (2)
According to Avogadro’s law,
= constant ………………. (3)
After combining equations (1), (2) and (3), you can get the following equation.
= constant …………….…. (4)
The above relation is called the combined law of gases. If you consider a gas, which contains μ moles of the gas, the number of atoms contained will be equal to p times the Avogadro number, NA
i.e. n = μNA ………………………. (5)
Using equation (5), equation (4) can be written as
PV/ μNAT = constant
The value of the constant in the above equation is taken to be kB, which is called as Boltzmann constant (1.38 × 10-23 JK-1).
Hence, we have the following equation:
PV / μNAT = kB
PV = μNAkBT
Here, μNAkB = R, which is termed as universal gas constant whose value is 8.31 J mol-1 K-1.
PV = RT ……………………. (6)
The ideal gas equation is also called an equation of state because it gives the relation between the state variables and it is used to describe the state of any gas.

2. Explain the experiment of measuring the real and apparent expansion of a liquid with a neat diagram.

 (i) To start with, the liquid whose real and apparent expansion is to be determined is poured in a container up to a level. Mark this level as L1.
(ii) Now, heat the container and the liquid using a burner as shown in the figure Initially, the container receives the thermal energy and it expands.
(iii) As a result, the volume of the liquid appears to have reduced. Mark this reduced level of liquid as L2.

On further heating, the thermal energy supplied to the liquid through the container results in the expansion of the liquid. Hence, the level of liquid rises to L3. Now, the difference between the levels L1 and L3 is called apparent expansion, and the difference between the levels L2 and L3 is called real expansion. The real expansion is always more than that of apparent expansion.
Real expansion = L3 – L2
Apparent expansion = L3 – L1.

IX. HOT Questions

1.If you keep ice at 0°C and water at 0°C in either of your hands, in which hand you will feel more chillness? Why?
Answer:
The hand having ice at 0°C will feel more chillness than of 0°C water.
Reason: The 0°C ice takes more heat from hand equal to mL, to convert 0°C Ice water, 0°C as compared to 0°C water of same mass. Hence m & L are the mass and latent heat of fusion of water respectively.