class 11 notes

Class 11 Physics Notes Chapter 11 (Chapter 11) – Lab Manual (English) Book

Philoid

Philoid

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Lab Manual (English)
Alright class, let's focus today on the key experiments and concepts covered in Chapter 11 of your Physics Lab Manual. This chapter primarily deals with Thermal Properties of Matter, focusing on experiments related to heat transfer, specific heat capacity, latent heat, and cooling. Understanding these experiments thoroughly is crucial, not just for your practical exams, but also as these concepts frequently appear in various government competitive exams.

Chapter 11: Thermal Properties of Matter (Experimental Aspects)

1. Key Concepts Recap:

  • Heat (Q): Energy transferred between systems due to a temperature difference. Unit: Joule (J), Calorie (cal). (1 cal = 4.186 J)
  • Temperature (T): Degree of hotness or coldness; related to the average kinetic energy of molecules. Unit: Kelvin (K), degree Celsius (°C). (T(K) = T(°C) + 273.15)
  • Specific Heat Capacity (s or c): The amount of heat required to raise the temperature of unit mass of a substance by one degree Celsius (or one Kelvin).
    • Formula: s = Q / (m * ΔT) or Q = m * s * ΔT
    • Unit: J kg⁻¹ K⁻¹ or cal g⁻¹ °C⁻¹
    • Water has a high specific heat capacity (approx. 4186 J kg⁻¹ K⁻¹ or 1 cal g⁻¹ °C⁻¹).
  • Heat Capacity (S): The amount of heat required to raise the temperature of a given body by one degree. S = m * s. Unit: J K⁻¹ or cal °C⁻¹.
  • Water Equivalent (W): The mass of water that would absorb or lose the same amount of heat as the body (e.g., calorimeter) for the same temperature change. W = m * s / s_water. If s_water = 1 cal g⁻¹ °C⁻¹, then W = m * s (numerically equal to heat capacity in CGS). Unit: kg or g.
  • Principle of Calorimetry (Method of Mixtures): When two bodies at different temperatures are brought into thermal contact, assuming no heat loss to the surroundings, the heat lost by the hotter body is equal to the heat gained by the colder body.
    • Heat Lost = Heat Gained
  • Latent Heat (L): The amount of heat absorbed or released during a change of state (phase transition) at a constant temperature, per unit mass.
    • Formula: Q = m * L
    • Unit: J kg⁻¹ or cal g⁻¹
    • Latent Heat of Fusion (L_f): Heat absorbed during melting (solid to liquid) or released during freezing (liquid to solid) at the melting point. For ice: approx. 3.34 × 10⁵ J kg⁻¹ or 80 cal g⁻¹.
    • Latent Heat of Vaporization (L_v): Heat absorbed during boiling (liquid to gas) or released during condensation (gas to liquid) at the boiling point. For water: approx. 2.26 × 10⁶ J kg⁻¹ or 540 cal g⁻¹.
  • Newton's Law of Cooling: The rate of loss of heat (-dQ/dt) of a body is directly proportional to the excess temperature of the body (T) over the surroundings (T₀), provided the temperature difference (T - T₀) is small.
    • -dQ/dt = k (T - T₀) where k is a constant depending on the nature and area of the surface.
    • Rate of fall of temperature: -dT/dt = (k / ms) (T - T₀) = K (T - T₀) where K = k / ms is another constant.

2. Common Experiments in Chapter 11:

Experiment 1: To determine the specific heat capacity of a given solid by the method of mixtures.

  • Aim: Find s_solid.
  • Apparatus: Calorimeter with stirrer and lid, insulating enclosure, thermometer, given solid (e.g., metal shots), water, balance, heating arrangement (heater/burner, beaker).
  • Theory: Based on the principle of calorimetry.
    Heat lost by hot solid = Heat gained by calorimeter + Heat gained by water.
    m_s * s_s * (T_1 - T) = (m_c * s_c + m_w * s_w) * (T - T_2)
    Where:
    • m_s, s_s, T_1: mass, specific heat, initial temp. of solid.
    • m_c, s_c: mass, specific heat of calorimeter (+stirrer).
    • m_w, s_w: mass, specific heat of water in calorimeter.
    • T_2: initial temp. of calorimeter + water.
    • T: final equilibrium temperature of the mixture.
      (Note: m_c * s_c can be replaced by W_c * s_w, where W_c is the water equivalent of the calorimeter)
  • Procedure Outline:
    1. Weigh the empty calorimeter + stirrer (m_c).
    2. Fill it about half/two-thirds with water, weigh again (m_c + m_w), find m_w.
    3. Measure initial temperature of calorimeter + water (T_2).
    4. Heat the solid sample in a beaker of boiling water or a heating tube to a steady high temperature (T_1, usually 100°C if boiled).
    5. Quickly transfer the hot solid into the calorimeter, stir gently.
    6. Record the highest steady temperature reached by the mixture (T).
    7. Weigh the calorimeter + contents to find the mass of the solid (m_s). (Alternatively, weigh the solid before heating).
  • Calculations: Rearrange the formula to find s_s.
  • Precautions:
    • Solid should be heated uniformly.
    • Transfer solid quickly without splashing.
    • Stir mixture gently to ensure uniform temperature.
    • Read temperatures accurately (avoid parallax error).
    • Use insulating lid and enclosure to minimize heat loss.
    • Solid should be insoluble in water and not react with it.
  • Sources of Error:
    • Heat loss during transfer of solid.
    • Heat loss to surroundings from calorimeter.
    • Inaccurate temperature/mass measurements.
    • Delay in reading the final temperature.

Experiment 2: To determine the specific heat capacity of a given liquid by the method of mixtures.

  • Aim: Find s_liquid.
  • Apparatus: Same as Exp 1, but the unknown is a liquid, and a known solid (e.g., copper or lead shots) is used as the hot body.
  • Theory:
    Heat lost by hot solid = Heat gained by calorimeter + Heat gained by the unknown liquid.
    m_solid * s_solid * (T_1 - T) = (m_c * s_c + m_liquid * s_liquid) * (T - T_2)
    (Symbols have usual meanings, adapted for this setup)
  • Procedure Outline: Similar to Exp 1, but the calorimeter contains the unknown liquid instead of water. Heat a known solid, transfer it to the liquid in the calorimeter, and measure temperatures.
  • Precautions & Errors: Similar to Exp 1, plus ensure the liquid doesn't evaporate significantly or react with the solid/calorimeter.

Experiment 3: To determine the latent heat of fusion of ice (L_f).

  • Aim: Find L_f for ice.
  • Apparatus: Calorimeter, stirrer, lid, thermometer, balance, beaker, blotting paper, ice pieces.
  • Theory:
    Heat lost by (calorimeter + warm water) = Heat gained by ice (melting) + Heat gained by melted ice (water).
    (m_c * s_c + m_w * s_w) * (T_1 - T) = m_ice * L_f + m_ice * s_w * (T - 0°C)
    Where:
    • T_1: initial temp. of calorimeter + warm water.
    • T: final equilibrium temperature (should be above 0°C).
    • m_ice: mass of ice melted.
    • 0°C is the melting point of ice.
  • Procedure Outline:
    1. Weigh empty calorimeter (m_c).
    2. Fill with warm water (around 30-40°C), weigh (m_c + m_w), find m_w.
    3. Record initial temperature (T_1).
    4. Take small pieces of ice, dry them with blotting paper.
    5. Add dry ice pieces slowly while stirring until the temperature falls (e.g., to 5-10°C). Ensure all ice melts.
    6. Record the lowest steady final temperature (T).
    7. Weigh the calorimeter + contents (m_c + m_w + m_ice), find m_ice.
  • Calculations: Rearrange the formula to find L_f.
  • Precautions:
    • Use dry ice pieces (blotting paper is essential).
    • Add ice slowly to ensure it melts completely before adding more.
    • Stir continuously.
    • Avoid splashing.
    • Final temperature should be sufficiently above 0°C.
    • Minimize heat exchange with surroundings.
  • Sources of Error:
    • Wet ice added (introduces error in m_ice and extra cooling).
    • Heat absorbed from surroundings.
    • Inaccurate measurements.

Experiment 4: To study the relationship between the temperature of a hot body and time by plotting a cooling curve.

  • Aim: Observe how a hot body cools over time and verify Newton's Law of Cooling (optional extension).
  • Apparatus: Calorimeter with stirrer, thermometer (preferably 0-100°C with 0.5°C least count), hot water (around 80-90°C), stopwatch, double-walled enclosure, clamp stand.
  • Procedure:
    1. Fill the calorimeter about two-thirds with hot water.
    2. Place it inside the double-walled enclosure (ensures constant surrounding temperature T₀).
    3. Suspend the thermometer and stirrer in the water.
    4. Start the stopwatch and record the water temperature at regular intervals (e.g., every 30 seconds or 1 minute).
    5. Stir the water gently before each reading.
    6. Continue recording until the temperature falls significantly (e.g., by 30-40°C).
    7. Record the constant temperature of the enclosure (T₀).
  • Observations & Graph:
    • Tabulate Time (t) vs Temperature (T).
    • Plot a graph of T (y-axis) vs t (x-axis). This is the cooling curve, which will be exponential in shape (steeper initially, flatter later).
  • Verification of Newton's Law (Optional):
    • Method 1: Calculate (T - T₀) for each reading. Plot log_e(T - T₀) vs t. If the law holds, this should be a straight line with a negative slope.
    • Method 2: Calculate the rate of fall of temperature (ΔT/Δt) for different temperature intervals. Plot ΔT/Δt vs (T_avg - T₀), where T_avg is the average temperature in that interval. This should be a straight line passing through the origin (approximately).
  • Precautions:
    • Ensure surrounding temperature (T₀) remains constant (use enclosure).
    • Stir gently and continuously for uniform temperature.
    • Start observations when the temperature is reasonably high but stable.
    • Temperature difference (T - T₀) should ideally not be excessively large for the law to hold accurately in its simple form.
  • Sources of Error:
    • Fluctuations in surrounding temperature.
    • Heat loss variations (e.g., due to drafts).
    • Inaccurate time/temperature readings.

3. Importance for Exams:

  • Understand the principles (Calorimetry, Latent Heat, Newton's Law).
  • Know the formulae and be able to apply them.
  • Recognize the apparatus used.
  • Be aware of the precautions and sources of error – these are common question areas.
  • Understand the shape of graphs (e.g., cooling curve) and what they represent.
  • Know the standard units for all quantities.

Multiple Choice Questions (MCQs):

  1. The principle of calorimetry states that, in an isolated system, the net heat change is:
    a) Positive
    b) Negative
    c) Zero
    d) Dependent on the substances mixed

  2. Water equivalent of a calorimeter is measured in:
    a) Joules
    b) Joules/Kelvin
    c) Kilograms
    d) No unit

  3. In the experiment to find the specific heat of a solid, the solid is heated in boiling water primarily to:
    a) Clean the solid
    b) Ensure it reaches a known, steady temperature (100°C)
    c) Increase its mass
    d) Make it react with the calorimeter water

  4. While determining the latent heat of fusion of ice, why must the ice pieces be dried with blotting paper before adding them to the calorimeter?
    a) To make the ice melt faster
    b) To prevent splashing
    c) To ensure only the mass of ice (and not adhering water) is measured and contributes to cooling via melting
    d) To increase the initial temperature of the ice

  5. Newton's Law of Cooling states that the rate of cooling is proportional to:
    a) The temperature of the body (T)
    b) The temperature of the surroundings (T₀)
    c) The difference in temperature between the body and surroundings (T - T₀)
    d) The specific heat capacity of the body

  6. A cooling curve is plotted between:
    a) Heat lost vs Time
    b) Temperature vs Time
    c) Rate of cooling vs Temperature
    d) Log(Temperature) vs Time

  7. Which of the following is a necessary precaution when determining specific heat capacity by the method of mixtures?
    a) Use a large amount of hot solid
    b) Ensure the final temperature is exactly halfway between initial temperatures
    c) Minimize heat loss to the surroundings using an insulating enclosure
    d) Heat the solid directly over a flame

  8. The unit J kg⁻¹ K⁻¹ represents:
    a) Latent Heat
    b) Heat Capacity
    c) Specific Heat Capacity
    d) Thermal Conductivity

  9. If m is the mass of steam condensed and L_v is the latent heat of vaporization, the heat released during condensation alone is given by:
    a) m * s_w * ΔT
    b) m * L_v
    c) m * L_v + m * s_w * ΔT
    d) m * L_f

  10. A possible source of error in the cooling curve experiment is:
    a) Using a thermometer with a small range
    b) Stirring the liquid continuously
    c) Fluctuation in the surrounding temperature
    d) Plotting temperature against time

Answers to MCQs:

  1. c) Zero
  2. c) Kilograms (or grams)
  3. b) Ensure it reaches a known, steady temperature (100°C)
  4. c) To ensure only the mass of ice (and not adhering water) is measured and contributes to cooling via melting
  5. c) The difference in temperature between the body and surroundings (T - T₀)
  6. b) Temperature vs Time
  7. c) Minimize heat loss to the surroundings using an insulating enclosure
  8. c) Specific Heat Capacity
  9. b) m * L_v
  10. c) Fluctuation in the surrounding temperature

Study these concepts and experimental details carefully. Pay attention to the precautions and sources of error, as they highlight the practical challenges and the underlying physics. Good luck with your preparation!

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