One calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water through 1 °C. Relationship with Joule: 1 calorie = 4.186 Joules.

Boyle's Law states that at a constant temperature, the volume of a given mass of gas is inversely proportional to its pressure. Mathematical expression: P ∝ 1/V ⟹ P × V = constant (when T is constant). For two states: P₁V₁ = P₂V₂.

Unit 3: Thermal Physics (வெப்ப இயற்பியல்)

Q: The value of universal gas constant is ________.

Answer: 8.31 J mol⁻¹ K⁻¹. Explanation: The universal gas constant (R) is the constant of proportionality in the ideal gas law PV = nRT. Its standard SI value is approximately 8.31 J mol⁻¹ K⁻¹ (or 8.314 J mol⁻¹ K⁻¹).

Q: If a substance is heated or cooled, the change in mass of that substance is ________.

Answer: zero. Explanation: According to the Law of Conservation of Mass, heating or cooling only changes the thermal energy and volume/state of the substance. Mass is an intrinsic quantity that remains constant during heating or cooling.

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

Answer: (a) or (b). Explanation: Linear expansion is one-dimensional expansion. Depending on how the rod or substance is oriented, expansion will occur along either the X-axis (or -X) or the Y-axis (or -Y), i.e., (a) or (b).

Q: Temperature is the average ________ of the molecules of a substance.

Answer: difference in T.E and P.E. Explanation: Total Energy (T.E) of molecules = Kinetic Energy (K.E) + Potential Energy (P.E). Therefore, K.E = T.E - P.E. Since temperature is proportional to the average translational kinetic energy of the molecules, it is the average difference in Total Energy and Potential Energy.

Q: In heat transformation, thermal energy always transfers from ________.

Answer: a body at higher temperature to a body at lower temperature. Explanation: Heat is thermal energy in transit. It spontaneously flows down a temperature gradient, from a region of higher temperature to a region of lower temperature until thermal equilibrium is attained.

Q: The value of Avogadro number is ________.

Answer: 6.023 × 10²³ / mol (or 6.023 × 10²³). Avogadro's number is defined as the total number of atoms or molecules contained in one mole of any substance.

Q: The temperature and heat are ________ quantities.

Answer: scalar. Both temperature and heat energy have magnitude only and do not possess directional properties.

Q: One calorie is the amount of heat energy required to raise the temperature of ________ of water through ________.

Answer: 1 gram, 1 °C. By definition, 1 calorie = 4.186 Joules of thermal energy.

அலகு 3: வெப்ப இயற்பியல் — Tamil Nadu Samacheer Kalvi Book Back Answers & Solutions

Authentic Samacheer Kalvi book-back solutions for Thermal Physics covering Boyle's Law, Charles's Law, Avogadro's Law, Ideal Gas Equation (PV = nRT), thermal expansion of solids and liquids, real vs apparent expansion, and numerical problems.

பாயில் விதி, சார்லஸ் விதி, அவகேட்ரோ விதி, நல்லியல்பு வாயுச் சமன்பாடு (PV = nRT), திட மற்றும் திரவப் பொருட்களின் வெப்ப விரிவு, உண்மை மற்றும் தோற்ற விரிவு, மற்றும் கணக்கீடுகளை உள்ளடக்கிய முழுமையான விடைக்குறிப்புகள்.

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📐 Important Formulas & Laws Quick Revision

Boyle's Law (பாயில் விதி): P × V = constant (at constant T) ⟹ P₁V₁ = P₂V₂ At constant temperature, the volume of a given mass of gas is inversely proportional to its pressure.
Charles's Law (Law of Volume) (சார்லஸ் விதி (பரும விதி)): V / T = constant (at constant P) ⟹ V₁ / T₁ = V₂ / T₂ At constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.
Avogadro's Law (அவகேட்ரோ விதி): V ∝ n (at constant P and T) ⟹ V / n = constant Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.
Ideal Gas Equation (நல்லியல்பு வாயுச் சமன்பாடு): P × V = n × R × T (or PV = k_B × N × T) R = 8.31 J mol⁻¹ K⁻¹ (Universal Gas Constant). Relates pressure, volume, temperature, and amount of gas.
Coefficient of Superficial Expansion (α_A) (பரப்பு விரிவுக் குணகம் (α_A)): ΔA / A₀ = α_A × ΔT ⟹ α_A = ΔA / (A₀ × ΔT) Ratio of increase in area to original area per degree rise in temperature. Unit: K⁻¹.
Coefficient of Cubical Expansion (α_V) (பரும விரிவுக் குணகம் (α_V)): ΔV / V₀ = α_V × ΔT ⟹ α_V = ΔV / (V₀ × ΔT) Ratio of increase in volume to original volume per degree rise in temperature. Unit: K⁻¹.

Part I: Choose the Correct Answer (1 Mark)

1. The value of universal gas constant is ________.

பொது வாயு மாறிலியின் மதிப்பு ________.

(a) 3.81 J mol⁻¹ K⁻¹
(b) 8.03 J mol⁻¹ K⁻¹
(c) 1.38 J mol⁻¹ K⁻¹
(d) 8.31 J mol⁻¹ K⁻¹ ✓ (Correct Answer)

Explanation: The universal gas constant (R) is the constant of proportionality in the ideal gas law PV = nRT. Its standard SI value is approximately 8.31 J mol⁻¹ K⁻¹ (or 8.314 J mol⁻¹ K⁻¹).

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

ஒரு பொருளை வெப்பப்படுத்தினாலோ அல்லது குளிர்வித்தாலோ அப்பொருளின் நிறையில் ஏற்படும் மாற்றம் ________.

(a) positive
(b) negative
(c) zero ✓ (Correct Answer)
(d) none of the above

Explanation: According to the Law of Conservation of Mass, heating or cooling only changes the thermal energy and volume/state of the substance. Mass is an intrinsic quantity that remains constant during heating or cooling.

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

ஒரு பொருளை வெப்பப்படுத்தினாலோ அல்லது குளிர்வித்தாலோ ஏற்படும் நீள் விரிவு எந்த அச்சின் வழியே நடைபெறும்?

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

Explanation: Linear expansion is one-dimensional expansion. Depending on how the rod or substance is oriented, expansion will occur along either the X-axis (or -X) or the Y-axis (or -Y), i.e., (a) or (b).

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

வெப்பநிலை என்பது ஒரு பொருளில் உள்ள மூலக்கூறுகளின் சராசரி ________ ஆகும்.

(a) difference in K.E and P.E
(b) sum of P.E and K.E
(c) difference in T.E and P.E ✓ (Correct Answer)
(d) kinetic energy (K.E)

Explanation: Total Energy (T.E) of molecules = Kinetic Energy (K.E) + Potential Energy (P.E). Therefore, K.E = T.E - P.E. Since temperature is proportional to the average translational kinetic energy of the molecules, it is the average difference in Total Energy and Potential Energy.

5. In heat transformation, thermal energy always transfers from ________.

வெப்பப் பரிமாற்றத்தில் வெப்ப ஆற்றல் எப்போதுமே ________.

(a) a body at higher temperature to a body at lower temperature ✓ (Correct Answer)
(b) a body at lower temperature to a body at higher temperature
(c) lower mass to higher mass
(d) higher volume to lower volume

Explanation: Heat is thermal energy in transit. It spontaneously flows down a temperature gradient, from a region of higher temperature to a region of lower temperature until thermal equilibrium is attained.

Part II: Fill in the Blanks (கோடிட்ட இடங்களை நிரப்புக)

1. The value of Avogadro number is ________.

அவகேட்ரோ எண்ணின் மதிப்பு ________.

Answer: 6.023 × 10²³ / mol (or 6.023 × 10²³) (6.023 × 10²³ / மோல்)

2. The temperature and heat are ________ quantities.

வெப்பநிலை மற்றும் வெப்பம் ஆகியவை ________ அளவுகள் ஆகும்.

Answer: scalar (ஸ்கேலார் (திசையிலா))

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

ஒரு கலோரி என்பது ________ நீரின் வெப்பநிலையை ________ உயர்த்த தேவையான வெப்ப ஆற்றலின் அளவு ஆகும்.

Answer: 1 gram, 1 °C (1 கிராம், 1 °C)

4. According to Boyle's law, the shape of the graph between pressure and reciprocal of volume (1/V) is ________.

பாயில் விதியின்படி, அழுத்தம் மற்றும் பருமனின் தலைகீழி (1/V) இடையேயான வரைபடம் ________ ஆகும்.

Answer: a straight line passing through the origin (நேர்க்கோடு (ஆதிப்புள்ளி வழியே செல்லும் நேர்க்கோடு))

Part III: State True or False with Statement Correction (சரியா? தவறா?)

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

ஒரு குறிப்பிட்ட வெப்பத்திற்கு, திரவத்தில் ஏற்படும் தோற்ற விரிவு உண்மை விரிவை விட அதிகம்.

✗ FALSE (தவறு)

Correct Statement: For a given heat in liquid, real expansion is always greater than apparent expansion (Real Expansion = Apparent Expansion + Expansion of Container).

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

வெப்ப ஆற்றல் எப்போதும் உயர் வெப்பநிலையிலுள்ள அமைப்பிலிருந்து குறைந்த வெப்பநிலையிலுள்ள அமைப்பிற்கு பாயும்.

✓ TRUE (சரி)

3. According to Charles's law, at constant pressure, the temperature is inversely proportional to volume.

சார்லஸ் விதியின்படி, மாறா அழுத்தத்தில் வெப்பநிலை பருமனுக்கு எதிர்த்தகவில் அமையும்.

✗ FALSE (தவறு)

Correct Statement: According to Charles's law, at constant pressure, the volume of a gas is directly proportional to its absolute temperature (V ∝ T).

Part IV: Match the Following (பொருத்துக)

Linear expansion (நீள் விரிவு) ➔ change in length
Superficial expansion (பரப்பு விரிவு) ➔ change in area
Cubical expansion (பரும விரிவு) ➔ change in volume
Heat transformation (வெப்பப் பரிமாற்றம்) ➔ hot body to cold body
Boltzmann constant (போல்ட்ஸ்மேன் மாறிலி) ➔ 1.381 × 10⁻²³ J K⁻¹

Part V: Assertion and Reason (கூற்றும் காரணமும்)

Question 1:

Assertion (A): If one end of a metal rod is heated, the other end also becomes heated.

Reason (R): Heat always flows from a region of lower temperature to higher temperature of the rod.

Correct Answer: (c) Assertion is true but reason is false

The assertion is true because metals conduct heat along their length. The reason is completely false because heat flows from higher temperature to lower temperature, not lower to higher.

Question 2:

Assertion (A): Gas is highly compressible than solid and liquid.

Reason (R): Interatomic or intermolecular distance in gas is comparably high.

Correct Answer: (a) Both assertion and reason are true and reason is the correct explanation of assertion

In gases, intermolecular spaces are large and intermolecular forces of attraction are negligible. Applying external pressure easily brings gas molecules closer together, making gases highly compressible.

Part VI: Short Answer Questions — 2 Marks (சுருக்கமான விடையளி)

Q1. Define one calorie.

ஒரு கலோரி வரையறு.

Answer:

One calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water through 1 °C.
Relationship with Joule: 1 calorie = 4.186 Joules.

Q2. Distinguish between linear, superficial and cubical expansion.

நீள் விரிவு, பரப்பு விரிவு மற்றும் பரும விரிவு வேறுபடுத்துக.

Answer:

1. Linear Expansion (α_L): Expansion in length of a solid body when heated. Formula: ΔL / L₀ = α_L × ΔT.
2. Superficial Expansion (α_A): Expansion in surface area of a solid body when heated. Formula: ΔA / A₀ = α_A × ΔT.
3. Cubical Expansion (α_V): Expansion in volume of a body when heated. Formula: ΔV / V₀ = α_V × ΔT.

Q3. What is coefficient of cubical expansion?

பரும விரிவுக் குணகம் என்றால் என்ன?

Answer:

The coefficient of cubical expansion is defined as the ratio of increase in volume of the body per degree rise in temperature to its unit original volume.
Formula: α_V = ΔV / (V₀ × ΔT)
SI Unit: K⁻¹ (per Kelvin).

Q4. State Boyle's law.

பாயில் விதியைக் கூறுக.

Answer:

Boyle's Law states that at a constant temperature, the volume of a given mass of gas is inversely proportional to its pressure.
Mathematical expression: P ∝ 1/V ⟹ P × V = constant (when T is constant).
For two states: P₁V₁ = P₂V₂.

Q5. State the law of volume (Charles's law).

சார்லஸ் விதி (பரும விதி) கூறுக.

Answer:

Charles's law (Law of Volume) states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.
Mathematical expression: V ∝ T ⟹ V / T = constant.
For two states: V₁ / T₁ = V₂ / T₂.

Q6. Distinguish between ideal gas and real gas.

நல்லியல்பு வாயு மற்றும் இயல்பு வாயு வேறுபடுத்துக.

Answer:

1. Ideal Gas: Obeys gas laws (PV = nRT) under all conditions of temperature and pressure. Intermolecular attraction and molecular volume are considered zero. (Theoretical concept).
2. Real Gas: Does not obey gas laws at all conditions; only behaves as an ideal gas at very low pressure and high temperature. Intermolecular forces and volume of molecules exist in reality.

Q7. What is coefficient of real expansion and coefficient of apparent expansion?

உண்மை விரிவுக் குணகம் மற்றும் தோற்ற விரிவுக் குணகம் வரையறு.

Answer:

Coefficient of Real Expansion: The ratio of true (actual) increase in volume of the liquid per degree rise in temperature to its unit volume at 0 °C. Unit: K⁻¹.
Coefficient of Apparent Expansion: The ratio of apparent increase in volume of the liquid (without accounting for container expansion) per degree rise in temperature to its unit volume at 0 °C. Unit: K⁻¹.

Part VII: Long Answer Questions — 5 / 7 Marks (விரிவான விடையளி)

Q1. Derive the ideal gas equation.

நல்லியல்பு வாயுச் சமன்பாட்டைத் தருவிக்கவும்.

1. Stating the Fundamental Gas Laws

According to Boyle's law: V ∝ 1/P (at constant T)
According to Charles's law: V ∝ T (at constant P)
According to Avogadro's law: V ∝ n (at constant P and T)

2. Combining the Gas Laws

Combining all three equations, we get:
V ∝ (n × T) / P
P × V ∝ n × T
PV = constant × n × T

3. Introducing Universal Gas Constant (R)

The constant of proportionality is called the Universal Gas Constant, denoted by R.
Therefore: PV = nRT
This is the Ideal Gas Equation (Equation of State for an ideal gas).
Here: P = Pressure, V = Volume, n = Number of moles, R = 8.31 J mol⁻¹ K⁻¹, T = Absolute Temperature in Kelvin.

Conclusion: Hence, the ideal gas equation PV = nRT relates the macroscopic properties (P, V, T) of an ideal gas.

Q2. Explain the experiment of measuring the real and apparent expansion of a liquid with a neat diagram.

ஒரு திரவத்தின் உண்மை விரிவு மற்றும் தோற்ற விரிவினை அளவிடும் சோதனையை தகுந்த படத்துடன் விவரி.

1. Experimental Setup

A liquid whose real and apparent expansions are to be determined is poured into a round-bottomed glass flask up to a level marked as L₁.
The flask is placed on a wire gauze over a tripod stand and heated using a burner.

2. Observations during Heating

Initial level: Marked as L₁.
Level after initial heating: The flask receives heat first and expands before heat reaches the liquid. Thus, the liquid level temporarily falls from L₁ to L₂.
Level on continued heating: The liquid absorbs heat and expands rapidly (since liquid expansion > glass expansion). The level rises to L₃.

3. Calculations

Apparent expansion = L₃ - L₁ (observed rise without considering flask expansion).
Real expansion = L₃ - L₂ (actual total expansion of the liquid).
Expansion of flask = L₁ - L₂.
Relationship: Real Expansion = Apparent Expansion + Flask Expansion (L₃ - L₂ = (L₃ - L₁) + (L₁ - L₂)).
Conclusion: Real expansion is always greater than apparent expansion.

Part VIII: Solved Problems Corner / Numerical Calculations

Problem 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 α_A = 0.0021 K⁻¹).

வெப்பப்படுத்துதலால் 10 m² குறுக்குவெட்டுப் பரப்புடைய செம்புத் தண்டு 11 m² ஆக மாறுகிறது. அதன் ஆரம்ப வெப்பநிலை 90 K எனில் அதன் இறுதி வெப்பநிலையைக் காண்க. (செம்பின் பரப்பு விரிவுக் குணகம் α_A = 0.0021 K⁻¹).

Step-by-Step Working:Step 1: Calculate temperature change ΔT:
ΔT = ΔA / (A₀ × α_A)
ΔT = 1 / (10 × 0.0021) = 1 / 0.021
ΔT = 1000 / 21 ≈ 47.62 K
Step 2: Calculate final temperature T₂:
ΔT = T₂ - T₁ ⟹ T₂ = T₁ + ΔT
T₂ = 90 K + 47.62 K = 137.62 K

                Boxed Final Answer: Final temperature T₂ = 137.62 K (or approximately 137.6 K)
              

Problem 2: Calculate the coefficient of cubical expansion of a zinc bar whose volume is increased by 0.25 m³ from 0.3 m³ due to the change in its temperature of 50 K.

0.3 m³ பருமனுடைய துத்தநாகத் தண்டு 50 K வெப்பநிலை மாற்றத்தால் 0.25 m³ பருமன் அதிகரிக்கிறது எனில் அதன் பரும விரிவுக் குணகத்தைக் கணக்கிடுக.

Step-by-Step Working:Step 1: Substitute values into formula:
α_V = 0.25 / (0.3 × 50)
α_V = 0.25 / 15
α_V = 25 / 1500 = 1 / 60 ≈ 0.01667 K⁻¹ (or 1.67 × 10⁻² K⁻¹)

                Boxed Final Answer: Coefficient of cubical expansion α_V = 0.0167 K⁻¹ (or 1.67 × 10⁻² K⁻¹)
              