## Science : Chapter 3 : Thermal Physics

## TEXTBOOK EVALUATION

*I. Choose the correct answer*

The value of universal gas constant

- 3.81 mol
^{–1}K^{–1} - 8.03 mol
^{–1}K^{–1} - 1.38 mol
^{–1}K^{–1} - 8.31 mol
^{–1}K^{–1}

Ans : 8.31 mol^{–1}K^{–1}

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

- positive
- negative
- zero
- none of the above

Ans : zero

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

- X or –X
- Y or –Y
- both (a) and (b)
- (a) or (b)

Ans : both (a) and (b)

4. Temperature is the average __________ of the molecules of a substance.

- difference in K.E and P.E
- sum of P.E and K.E
- difference in T.E and P.E
- difference in K.E and T.E

Ans : difference in T.E. and P.E

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

- A ← B, A ← C, B ← C
- A → B, A → C, B → C
- A → B, A ← C, B → C
- A ← B, A → C, B ← C

Ans : A ← B, A ← C, B ← C

*II. Fill in the blanks:*

1. The value of Avogadro number __________.

Ans : 6.023 × 10^{23}/mol

2. The temperature and heat are __________ quantities.

Ans : Scalar

3. One calorie is the amount of heat energy required to raise the temperature of __________ of water through __________.

Ans : 1g ; 1°C

4. According to Boyle’s law, the shape of the graph between pressure and reciprocal of volume is __________.

Ans : 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. ( False )

- For a given heat in liquid, the real expansion is more or less than that of apparent expansion.

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

temperature. ( True )

3. According to Charles’s law, at constant pressure, the temperature is inversely proportional to volume. ( False )

- According to Charles’s law, at constant pressure, the volume is directly proportional to temperature.

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

Column – I | Column – II |

1) Linear expansion | a) change in volume |

2) Superficial expansion | b) hot body to cold body |

3) Cubical expansion | c) 1.381 X 10^{–23} JK^{–1} |

4) Heat transformation | d) change in length |

5) Boltzmann constant | e) change in area |

**Ans ; 1 – d, 2 – e, 3 – a, 4 -b, 5 – c**

*V. Assertion and reason type questions*

- Both the assertion and the reason are true and the reason is the correct explanation of the assertion.
- Both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
- Assertion is true but the reason is false.
- Assertion is false but the reason is true.

1. **Assertion**: There is no effects on other end when one end of the rod is only heated.**Reason**: Heat always flows from a region of lower temperature to higher temperature of the rod.

- Ans ; Assertion is true but the reason is false.

2. **Assertion**: Gas is highly compressible than solid and liquid**Reason**: Interatomic or intermolecular distance in the gas is comparably high.

- Ans ; Assertion is true but the reason is false.

*VI. Book Exercise – Answer in briefly*

1. Define one calorie.

Calorie: One calorie is defined as the amount of heat energy required to rise the temperature of 1 gram of water through 1°C.

2. Distinguish between linear, arial or superficial expansion and Cubical Expansion.

Linear Expansion | Arial Expansion | Cubical Expansion |

When a body is heated or cooled, the length of the body changes due to change in its temperature. Then the expansion is said to be linear or longitudinal expansion | If there is an increase in the area of a solid object due to heating, then the expansion is called superficial or areal expansion | If there is an increase in the volume of a solid body due to heating, then the expansion is called cubical or volumetric expansion. |

ΔV/L_{o} = α_{L}ΔT | ΔA/A_{o} = α_{A}ΔT | ΔV/V_{o} = α_{v}ΔT |

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}. α_{v} = ΔV / V_{o} Δ T

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.

P α 1/V

In other words, for an invariable mass of a perfect gas, at constant temperature, the product of its pressure and volume is a constant.

(i.e) PV = constant

5. State-Charles law of volume.

Charles’s law was formulated by a French scientist Jacques Charles. 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 α T

V / T = constant.

6. Distinguish between ideal gas and real gas.

IDEAL GAS | REAL GAS |

If the atoms or molecules of a gas do not interact with each other, then the gas is said to be an ideal gas or a perfect gas.when the pressure is low or the temperature is high because the interatomic or intermolecular forces of attraction are weak in ideal gas. Hence, a real gas at low pressure or high temperature can be termed as a perfect gas. | If the molecules or atoms of a gases interact with each other with a definite amount of intermolecular or inter atomic force of attraction, then the gases are said to be real gases.At very high temperature or low pressure, a real gases behaves as an ideal gases because in this condition there is no interatomic or intermolecular force of attraction. |

7. What is 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 apparant 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 m^{2 }to 11 m^{2} due to heating. The copper rod is initially kept at 90K. (Coefficient of superficial expansion is 0.0021 /K)

Solution :

Given : Ti = 90k, A = 10m^{2 }, ΔA = 11-10 = 1m^{2}, Tf = ? | |

ΔA / AΔA / A1 / 10T_{f}T_{f} | = α_{A} ΔT= α_{A} (T_{f }– T_{i)}= 0.0021 ( T_{f }– 90)= 2890/21= 137.6 K |

2. Calculate the coefficient of cubical expansion of a zinc bar. Whose volume is increased 0.25 m^{3} from 0.3 m^{3} due to the change in its temperature of 50K.

Solution :

Given : ΔT = 50K, V=0.03m^{3}, ΔV = 0.55-0.3m^{3}, α_{v}= ? | |

ΔV / Vα_{V}α_{V}α_{V} | = α_{A} ΔT= ΔV / VΔT= 0.25/0.3×50 = 0.25/15= 0.0166 K^{-1} |

*VIII. Answer in detail*

1. Derive the ideal gas equation.

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,

V / T = constant → 2

According to Avogadro’s law,

V/n = constant → 3

After combining equations (1), (2) and (3), we can get the following equation.

PV/_{n}T = 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 μ times the Avogadro number, N_{A}.

i.e. n = μN_{A} 5

Using equation (5), equation (4) can be written as

PV / μN_{A}T = 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 / μN_{A}T = k_{B}

PV = μN_{A} k_{B} T

Here, μNAKB = R, which is termed as universal gas constant whose value is 8.31 J mol^{−1}K^{−1}.

PV = RT → 6

Ideal gas equation is also called as 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.

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 L_{1}.

Now, heat the container and the liquid using a burner.

Initially, the container receives the thermal energy and it expands. As a result, the volume of the liquid appears to have reduced. Mark this reduced level of liquid as L_{2}.

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 L_{3}. Now, the difference between the levels L_{1} and L_{3} is called as apparent expansion, and the difference between the levels L_{2} and L_{3} is called real expansion. The real expansion is always more than that of apparent expansion.

Real expansion = L_{3} – L_{2} Apparent expansion = L_{3} – L_{1}.

*IX. HOT question*

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?

Ice transfer more chillness to our hands than water. Due to thermal conduction in between ice and environment. The latent heat of vaporisation for ice is more than water at 0º c.