Class 11 Physics Notes Chapter 8 (Chapter 8) – Lab Manual (English) Book

Detailed Notes with MCQs of Experiment 8 from your Lab Manual, which deals with the cooling of a hot body. This is an important concept often tested in government exams, primarily focusing on Newton's Law of Cooling.

Experiment 8: To study the relationship between the temperature of a hot body and time by plotting a cooling curve.

1. Aim:
To observe how the temperature of a hot body (like water in a calorimeter) decreases over time and to plot a graph representing this relationship (the cooling curve). This study helps in understanding and verifying Newton's Law of Cooling.

2. Apparatus Required:

• Calorimeter with a stirrer
• A double-walled enclosure (to ensure cooling occurs in a uniform environment)
• Two thermometers (0-100°C range, preferably with 0.5°C or 0.1°C least count)
• Stopwatch
• Heating arrangement (like a burner or heater)
• Beaker, Water, Clamp stand

3. Theory:

• Cooling: The process by which a body loses heat energy to its surroundings, resulting in a decrease in its temperature.

• Newton's Law of Cooling: This fundamental law states that, for small temperature differences between a body and its surroundings, the rate of loss of heat by the body is directly proportional to the temperature difference between the body and the surroundings.

  • Conditions: The law holds good primarily when:

    • The temperature difference (T - T₀) is relatively small (typically < 30-40°C).
    • Heat loss is mainly due to convection and radiation (forced convection like strong air currents should be avoided).
    • The temperature of the surroundings (T₀) remains constant.
    • The surface properties (emissivity) and surface area of the body remain constant.

  • Mathematical Form:
    Rate of loss of heat, dQ/dt ∝ (T - T₀)
    Where:
    dQ/dt = Rate at which heat is lost
    T = Temperature of the body at any time 't'
    T₀ = Temperature of the surroundings (ambient temperature)

    Also, the heat lost dQ causes a temperature drop dT in the body.
    dQ = ms dT (where m = mass, s = specific heat capacity)
    Since heat is lost, dT is negative, so we consider the rate of fall of temperature:
    Rate of fall of temperature, -dT/dt = (1/ms) dQ/dt
    Combining these, -dT/dt ∝ (T - T₀)
    or dT/dt = -k (T - T₀)
    Here, k is a positive constant that depends on the nature of the surface, the surface area of the body, and its specific heat capacity. dT/dt represents the rate of cooling (fall in temperature per unit time).

• Cooling Curve (T vs t): A graph plotted with the temperature (T) of the body on the y-axis and time (t) on the x-axis.

  • The shape of this curve is an exponential decay. The rate of cooling (slope of the tangent to the curve) is steeper initially when the temperature difference (T - T₀) is large and becomes less steep as the body cools down and approaches the surrounding temperature.

• Verification Graph (logₑ(T - T₀) vs t):
  Integrating the equation dT/dt = -k (T - T₀), we get:
  ∫ dT / (T - T₀) = -∫ k dt
logₑ(T - T₀) = -kt + C (where C is the integration constant)
  This equation is in the form y = mx + c, representing a straight line.
  Therefore, a graph plotted with logₑ(T - T₀) on the y-axis and time t on the x-axis should be a straight line with a negative slope equal to -k. Plotting this graph verifies Newton's Law of Cooling. (Note: Using log₁₀ will also yield a straight line, but the slope will be -k / 2.303).

4. Procedure Outline:

1. Measure the room temperature (T₀) using one thermometer.
2. Heat water in a beaker to about 80°C - 90°C.
3. Fill the calorimeter about two-thirds full with the hot water.
4. Place the calorimeter inside the double-walled enclosure.
5. Suspend the second thermometer in the calorimeter water, ensuring the bulb is fully immersed. Place the stirrer.
6. Note the initial temperature (e.g., 80°C) and simultaneously start the stopwatch.
7. Record the temperature at regular intervals (e.g., every 1 minute). Stir the water gently before taking each reading to ensure uniform temperature.
8. Continue recording until the temperature falls significantly (e.g., down to 50°C or for about 30 minutes).
9. Note the final room temperature and use the average value for T₀ if it has changed slightly.

5. Observations & Calculations:

• Record the least count of the thermometer and stopwatch.
• Record the constant room temperature, T₀.
• Create a table with columns: Time (t), Temperature (T), Temperature Difference (T - T₀), logₑ(T - T₀).
• Plot the graphs:
  • T vs t (Cooling Curve)
  • logₑ(T - T₀) vs t (Verification Graph)

6. Results:

• The cooling curve (T vs t) shows that the rate of cooling decreases as time passes (curve becomes less steep).
• The graph of logₑ(T - T₀) vs t is found to be a straight line with a negative slope, which verifies Newton's Law of Cooling within the experimental limits.

7. Precautions:

• The enclosure should shield the calorimeter from air currents.
• Stir the liquid gently before each reading for uniform temperature.
• The thermometer bulb should be fully immersed but not touch the calorimeter walls or base.
• Start the stopwatch immediately when the first temperature reading is taken.
• Ensure the temperature difference (T - T₀) is not excessively large for better validity of the law.
• Note the room temperature accurately.

8. Importance for Exams:

• Understand the statement and conditions for Newton's Law of Cooling.
• Know the mathematical form: dT/dt = -k (T - T₀).
• Recognize the shape of the T vs t graph (exponential decay).
• Recognize the shape of the logₑ(T - T₀) vs t graph (straight line, negative slope).
• Understand factors affecting the cooling constant 'k' (surface area, nature of surface/emissivity, specific heat capacity, mass). A larger 'k' means faster cooling.
• Problems might involve comparing cooling rates of two identical bodies at different temperatures or two different bodies at the same initial temperature difference.

Multiple Choice Questions (MCQs):

1. Newton's Law of Cooling states that the rate of loss of heat is directly proportional to the:
   a) Temperature of the body
   b) Temperature of the surroundings
   c) Difference in temperature between the body and surroundings
   d) Specific heat capacity of the body

2. The cooling curve (Temperature vs Time) for a hot body cooling according to Newton's Law is:
   a) A straight line with a negative slope
   b) A parabola
   c) An exponential decay curve
   d) A hyperbolic curve

3. For Newton's Law of Cooling to be strictly applicable, the temperature difference between the body and surroundings should be:
   a) Very large
   b) Small
   c) Zero
   d) Any value

4. A graph is plotted between logₑ(T - T₀) and time 't', where T is the temperature of the body and T₀ is the surrounding temperature. According to Newton's Law of Cooling, this graph should be:
   a) A straight line passing through the origin
   b) An exponential curve
   c) A straight line with a negative slope
   d) A straight line with a positive slope

5. Two identical spheres, one coated black and the other polished silver, are heated to the same temperature and allowed to cool in the same environment. Which one will cool faster?
   a) Polished silver sphere
   b) Black coated sphere
   c) Both will cool at the same rate
   d) Cooling rate depends on the initial temperature only

6. The constant 'k' in the equation dT/dt = -k (T - T₀) depends on:
   a) Only the surface area of the body
   b) Only the nature of the surface (emissivity)
   c) Only the specific heat capacity and mass
   d) All of the above (surface area, emissivity, mass, specific heat capacity)

7. If a liquid takes 5 minutes to cool from 80°C to 70°C and 10 minutes to cool from 70°C to 60°C in the same surroundings, it indicates that:
   a) Newton's Law of Cooling is being followed
   b) Newton's Law of Cooling is not being followed
   c) The surrounding temperature is decreasing
   d) The specific heat capacity is changing

8. During the experiment on cooling, stirring the liquid ensures:
   a) Faster cooling
   b) Slower cooling
   c) Uniform temperature distribution within the liquid
   d) Prevention of heat loss by conduction

9. The slope of the tangent to the cooling curve (T vs t) at any point represents:
   a) The total heat lost
   b) The instantaneous rate of cooling (-dT/dt)
   c) The cooling constant 'k'
   d) The temperature difference (T - T₀)

10. If the surrounding temperature (T₀) increases while a body is cooling, the rate of cooling of the body will:
    a) Increase
    b) Decrease
    c) Remain constant
    d) Become zero instantly

Answer Key for MCQs:

1. c
2. c
3. b
4. c
5. b (Black surfaces are better emitters/absorbers of radiation)
6. d
7. a (Rate of cooling decreases as temperature difference decreases)
8. c
9. b
10. b (Because the temperature difference (T - T₀) decreases)

Study these notes carefully, focusing on the concepts and the graphical representations. Good luck with your preparation!