Your Progress — Chapter 3: Thermal Physics
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MCQI. Multiple Choice Questions1 mark each
Q.1 The value of universal gas constant
✓ Answer: (D) 8.31 J mol^-1 K^-1 (approximately 8.314 J mol^-1 K^-1).
Q.2 If a substance is heated or cooled, the change in mass of that substance is
✓ Answer: (C) zero
Q.3 If a substance is heated or cooled, the linear expansion occurs along the axis of
✓ Answer: (A) X or -X
Q.4 Temperature is the average ___________ of the molecules of a substance
✓ Answer: (C) difference in T.E and P.E. Since T.E = K.E + P.E, K.E = T.E - P.E; temperature is related to the average kinetic energy of molecules.
Q.5 In the Given diagram, the possible direction of heat energy transformation is
✓ Answer: (A) A ← B, A ← C, B ← C. In the textbook diagram, C is at the highest temperature, B is next, and A is at the lowest temperature. Heat flows from higher temperature to lower temperature, so C → B, C → A and B → A.
FillII. Fill in the Blanks1 mark each
| # | Statement (Answer in bold) |
|---|---|
| 1 | The value of Avogadro number 6.023 x 1023 / mol (or) mol-1 |
| 2 | The temperature and heat are Scalar quantities |
| 3 | One calorie is the amount of heat energy required to raise the temperature of 1 gm of water through 1^\circ C. |
| 4 | According to Boyle's law, the shape of the graph between pressure and reciprocal of volume is straight line |
T/FIII. True or False1 mark each
| # | Statement | Answer | Correction (if False) |
|---|---|---|---|
| 1 | For a given heat in liquid, the apparent expansion is more than that of real expansion. | False | Real expansion is greater than apparent expansion because the container also expands when heated. |
| 2 | Thermal energy always flows from a system at higher temperature to a system at lower temperature. | True | Heat flows naturally from a hotter body to a colder body. |
| 3 | According to Charles’s law, at constant pressure, the temperature is inversely proportional to volume. | False | At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: V ∝ T. |
MatchIV. Match the Following1 mark each
| Column A | Column B |
|---|---|
| Linear expansion | Change in length |
| Superficial expansion | Change in area |
| Cubical expansion | Change in volume |
| Heat transformation | Hot body to cold body |
| Boltzmann constant | 1.380649 x 10^-23 J K^-1 |
A&RV. Assertion & Reasoning2 marks each
Q.1
Assertion: If one end of the rod is heated,other end also is heated.
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✓ Answer
Heat conduction transfers energy from the hot end to the cooler end of the rod until temperatures equalize. The correct direction of natural heat flow is from hot -> cold.
Q.2
Assertion: Gas is highly compressible than solid and liquid
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✓ Answer
Because intermolecular distances in gases are large, applying pressure reduces these distances significantly, making gases easily compressible compared with solids and liquids.
ShortVI. Short Answer Questions2 marks each
Q.1
Define one calorie.
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✓ Answer
Definition: 1 cal = heat needed to raise 1 g water by 1 °C. Conversion: 1 cal = 4.184 J (approx).
Q.2
Distinguish between linear, cubical and superficial expansion.
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✓ Answer
Linear expansion: change in length of a body due to change in temperature. Formula: Delta L = α L0 Delta T; unit of α is K^-1.
Cubical expansion: change in volume of a body due to change in temperature. Formula: Delta V = γ V0 Delta T; unit of γ is K^-1 and, for solids, γ is approximately 3α.
Superficial expansion: change in area of a body due to change in temperature. Formula: Delta A = β A0 Delta T; unit of β is K^-1 and, for solids, β is approximately 2α.
Cubical expansion: change in volume of a body due to change in temperature. Formula: Delta V = γ V0 Delta T; unit of γ is K^-1 and, for solids, γ is approximately 3α.
Superficial expansion: change in area of a body due to change in temperature. Formula: Delta A = β A0 Delta T; unit of β is K^-1 and, for solids, β is approximately 2α.
Q.1
Also called longitudinal expansion
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✓ Answer
Linear expansion is also called longitudinal expansion. Its formula is Delta L = α L0 Delta T, where Delta L is change in length, L0 is original length, Delta T is temperature change, and α is the coefficient of linear expansion with unit K^-1.
Q.1
Also called as superficial expansion
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✓ Answer
Areal expansion is also called superficial expansion. Its formula is Delta A = β A0 Delta T, so β = Delta A/(A0 Delta T). For solids, β is approximately 2α. Unit: K^-1.
Q.3
What is co-efficient of cubical expansion?
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✓ Answer
γ = Delta V/(V0 Delta T). For solids and liquids γ approx. 3α, where α is the linear coefficient. Unit of γ is K^-1.
Q.4
State Boyle’s law
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✓ Answer
P proportional to 1/V => P1V1 = P2V2 (for the same gas mass at constant temperature).
Q.5
State-the law of volume
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✓ Answer
If initial state (V1, T1) changes to (V2, T2) at constant pressure: V1/T1 = V2/T2. Units: V in m3 (or L), T in K.
Q.6
Distinguish between ideal gas and real gas.
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✓ Answer
Ideal gas: It obeys the ideal gas equation PV = nRT. Its molecules are assumed to have negligible volume and no intermolecular force of attraction.
Real gas: Its molecules have finite volume and intermolecular force of attraction. It obeys PV = nRT only approximately, especially at low pressure and high temperature. At high pressure and low temperature, it deviates from ideal behaviour.
Real gas: Its molecules have finite volume and intermolecular force of attraction. It obeys PV = nRT only approximately, especially at low pressure and high temperature. At high pressure and low temperature, it deviates from ideal behaviour.
Q.1
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.
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✓ Answer
An ideal gas, or perfect gas, is a gas whose molecules are assumed not to interact with each other and whose molecular volume is negligible. It obeys the ideal gas equation PV = nRT, where T is measured in kelvin.
Q.2
Ideal gas does not have volume.
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✓ Answer
The statement that ideal gas does not have volume is a simplification based on the ideal-gas model. In this theoretical model, the gas molecules themselves are considered to be point masses, meaning they have mass but occupy no space; their volume is assumed to be negligible or zero. This assumption simplifies calculations and helps in understanding the behavior of gases under certain conditions, particularly at low pressures and high temperatures. However, it is important to remember that this is an idealization, and real gas molecules do occupy a finite volume.
Q.1
If the molecules or atoms of a . gas interact with each other with a definite amount of intermolecular or inter atomic force of attraction, then the gas is said to be a real gas.
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✓ Answer
When the molecules or atoms of a gas interact with each other through a definite amount of intermolecular or interatomic force of attraction, the gas is classified as a real gas. Unlike the idealized scenario of an ideal gas, the molecules in a real gas are not point masses; they possess finite size and therefore occupy a definite volume. Furthermore, these molecules exert attractive forces on each other, which can influence the gas's behavior, especially at high pressures and low temperatures, causing deviations from ideal gas laws.
Q.2
Real gas has volume.
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✓ Answer
True. Molecules of a real gas possess finite dimensions and thus occupy space, meaning they have a definite molecular volume. This is a key distinction from the ideal-gas model, where the volume of the molecules themselves is neglected and considered to be zero. The finite volume occupied by real gas molecules becomes significant under conditions of high pressure, where the molecules are forced closer together, and the space they occupy can no longer be ignored in thermodynamic calculations.
Q.7
What is co-efficient of real expansion?
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✓ Answer
Let initial volume = V, true increase in volume = Delta V_real for a temperature change Delta T. Then γ = Delta V_real / (V x Delta T). In differential form dV = γ V dT, and for Delta T = 1 K, γ = Delta V_real / V. SI unit: K^-1.
Q.8
What is co-efficient of apparent expansion?
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✓ Answer
Coefficient of apparent expansion is the ratio of the apparent increase in volume of a liquid per degree rise in temperature to its original volume. Formula: γ_app = Delta V_apparent / (V Delta T). Since the container also expands, γ_app = γ_liquid - γ_container. Unit: K^-1 or °C^-1.
NumericalVII. Numerical Problems3 marks each
Q.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)
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✓ Answer
Given: A1 = 10 m2, A2 = 11 m2, T1 = 90 K, β = 0.0021 K^-1.
Delta A/A = (A2-A1)/A1 = 1/10 = 0.1.
Delta T = (Delta A/A)/β = 0.1/0.0021 approx. 47.619 K.
T2 = T1 + Delta T = 90 + 47.619 approx. 137.619 K approx. 137.6 K.
Delta A/A = (A2-A1)/A1 = 1/10 = 0.1.
Delta T = (Delta A/A)/β = 0.1/0.0021 approx. 47.619 K.
T2 = T1 + Delta T = 90 + 47.619 approx. 137.619 K approx. 137.6 K.
Q.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.
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✓ Answer
Given: V = 0.3 m^3, Delta V = 0.25 m^3, Delta T = 50 K.
Formula for cubical expansion: Delta V = γ V Delta T, so γ = Delta V / (V Delta T).
Calculation: γ = 0.25 / (0.3 x 50) = 0.25 / 15 = 0.0166667 K^-1.
Therefore, the coefficient of cubical expansion γ = 1.67 x 10^-2 K^-1.
Formula for cubical expansion: Delta V = γ V Delta T, so γ = Delta V / (V Delta T).
Calculation: γ = 0.25 / (0.3 x 50) = 0.25 / 15 = 0.0166667 K^-1.
Therefore, the coefficient of cubical expansion γ = 1.67 x 10^-2 K^-1.
LongVIII. Long Answer Questions5 marks each
Q.1
Derive the ideal gas equation.
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✓ Answer
(1) Boyle's law: for fixed amount and temperature, P proportional to 1/V => PV = constant.
(2) Charles's law: for fixed amount and pressure, V proportional to T => V/T = constant.
(3) Avogadro's law: at fixed P and T, V proportional to n => V/n = constant.
(4) Combining these gives V proportional to nT/P => PV proportional to nT => PV/(nT) = constant.
(5) For amount expressed in moles, the constant is the universal gas constant R, so:
PV = nRT (ideal gas equation)
(6) If amount is expressed as number of molecules N, then the constant is Boltzmann's constant k_B and:
PV = N k_B T
(7) Relation between constants: R = N_A k_B, where N_A = 6.022x10^23 mol^-1.
(8) Values and units: R = 8.314 J mol^-1 K^-1; k_B = 1.381x10^-23 J K^-1.
Note: Use consistent symbols: n for moles, N for molecules, and include n on the RHS of PV = nRT.
(2) Charles's law: for fixed amount and pressure, V proportional to T => V/T = constant.
(3) Avogadro's law: at fixed P and T, V proportional to n => V/n = constant.
(4) Combining these gives V proportional to nT/P => PV proportional to nT => PV/(nT) = constant.
(5) For amount expressed in moles, the constant is the universal gas constant R, so:
PV = nRT (ideal gas equation)
(6) If amount is expressed as number of molecules N, then the constant is Boltzmann's constant k_B and:
PV = N k_B T
(7) Relation between constants: R = N_A k_B, where N_A = 6.022x10^23 mol^-1.
(8) Values and units: R = 8.314 J mol^-1 K^-1; k_B = 1.381x10^-23 J K^-1.
Note: Use consistent symbols: n for moles, N for molecules, and include n on the RHS of PV = nRT.
Q.2
Explain the experiment of measuring the real and apparent expansion of a liquid with a neat diagram.
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✓ Answer
Apparatus: small flask (or bulb) fitted with a narrow capillary tube, wooden or metal stand, scale/ruled glass behind the capillary (for marking heights), thermometer, burner.
Procedure:
1. Fill the flask with the liquid up to a mark on the capillary and glass scale. Mark the initial level as L1 at room temperature and note the initial temperature T1.
2. Heat the flask gently. As the vessel (container) expands its internal volume increases and the liquid level in the capillary may fall slightly. When this fall is observed, mark this level as L2.
3. Continue heating so the liquid itself expands; the liquid level then rises and finally stabilises at L3 for a higher temperature T2.
Observations and definitions:
- Apparent expansion of the liquid = observed change relative to the original mark = L3 - L1.
- Real (actual) expansion of the liquid = change of liquid level excluding container expansion = L3 - L2.
- Therefore: Real = Apparent + (L1 - L2), where (L1 - L2) represents the change due to container expansion (drop in level).
Relation between coefficients:
- Let γ_liquid be the coefficient of cubical expansion of the liquid, γ_container that of the container, and γ_apparent the apparent coefficient observed.
- γ_apparent = γ_liquid - γ_container.
- Since the container is a solid, γ_container approx. 3α (α is the linear coefficient of the container).
- Hence γ_liquid = γ_apparent + 3α.
Formulas for a temperature change Delta T = (T2 - T1):
- Real volume increase Delta V_real = V0 γ_liquid Delta T.
- Apparent volume increase Delta V_apparent = V0 (γ_liquid - γ_container) Delta T.
Notes for exam answers:
- Label the neat diagram: flask/bulb, capillary tube, scale, L1, L2, L3, thermometer, burner.
- Give units: coefficients in °C^-1 (per degree Celsius) and volume in m3 (or cm3) when needed.
- State conclusion: real expansion of a liquid is greater than its apparent expansion because the container also expands.
Procedure:
1. Fill the flask with the liquid up to a mark on the capillary and glass scale. Mark the initial level as L1 at room temperature and note the initial temperature T1.
2. Heat the flask gently. As the vessel (container) expands its internal volume increases and the liquid level in the capillary may fall slightly. When this fall is observed, mark this level as L2.
3. Continue heating so the liquid itself expands; the liquid level then rises and finally stabilises at L3 for a higher temperature T2.
Observations and definitions:
- Apparent expansion of the liquid = observed change relative to the original mark = L3 - L1.
- Real (actual) expansion of the liquid = change of liquid level excluding container expansion = L3 - L2.
- Therefore: Real = Apparent + (L1 - L2), where (L1 - L2) represents the change due to container expansion (drop in level).
Relation between coefficients:
- Let γ_liquid be the coefficient of cubical expansion of the liquid, γ_container that of the container, and γ_apparent the apparent coefficient observed.
- γ_apparent = γ_liquid - γ_container.
- Since the container is a solid, γ_container approx. 3α (α is the linear coefficient of the container).
- Hence γ_liquid = γ_apparent + 3α.
Formulas for a temperature change Delta T = (T2 - T1):
- Real volume increase Delta V_real = V0 γ_liquid Delta T.
- Apparent volume increase Delta V_apparent = V0 (γ_liquid - γ_container) Delta T.
Notes for exam answers:
- Label the neat diagram: flask/bulb, capillary tube, scale, L1, L2, L3, thermometer, burner.
- Give units: coefficients in °C^-1 (per degree Celsius) and volume in m3 (or cm3) when needed.
- State conclusion: real expansion of a liquid is greater than its apparent expansion because the container also expands.
HOTIX. Higher Order Thinking3 marks each
Refer to textbook for answers.
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