To find the specific heat by the method of mixture using polystyrene cups (used as container of negligible heat capacity)

 

Abstract

This experiment aims to determine the specific heat of a substance by the method of mixture using polystyrene cups as containers of negligible heat capacity. By mixing known quantities of hot and cold water and measuring the final temperature, the specific heat of the substance can be calculated.

Introduction

The specific heat of a substance is the amount of heat required to raise the temperature of one unit mass of the substance by one degree Celsius. In this experiment, we use the method of mixture to find the specific heat of a substance. By mixing known quantities of hot and cold water in polystyrene cups, which have negligible heat capacity, and measuring the final temperature, we can calculate the specific heat of the substance.

Procedure

1. Measure the mass (\( m_1 \)) and initial temperature (\( \theta_1 \)) of the hot water.
2. Measure the mass (\( m_2 \)) and initial temperature (\( \theta_2 \)) of the cold water.
3. Pour the hot water into a polystyrene cup and record its mass (\( m_1' \)).
4. Pour the cold water into another polystyrene cup and record its mass (\( m_2' \)).
5. Stir the water in both cups and record the final temperature (\( \theta_f \)).

Observations and Calculations

Assume the following observations were made during the experiment:

• Mass of hot water (\( m_1 \)): 200 g
• Initial temperature of hot water (\( \theta_1 \)): 80°C
• Mass of cold water (\( m_2 \)): 150 g
• Initial temperature of cold water (\( \theta_2 \)): 20°C
• Final temperature of mixture (\( \theta_f \)): 30°C
• Specific heat of water: \( 4.18 \, \text{J/g} \cdot \text{°C} \)

The specific heat (\( c \)) of the substance can be calculated using the formula:

\( c = \frac{{m_1 \cdot c_{\text{water}} \cdot (\theta_1 - \theta_f) + m_2 \cdot c_{\text{water}} \cdot (\theta_f - \theta_2)}}{{m_1' \cdot (\theta_f - \theta_1) + m_2' \cdot (\theta_f - \theta_2)}} \)

Where \( c_{\text{water}} \) is the specific heat of water and \( m_1' \) and \( m_2' \) are the masses of the cups with water.

Conclusion

The experiment successfully demonstrates the method of mixture to find the specific heat of a substance. By mixing known quantities of hot and cold water in polystyrene cups and measuring the final temperature, we can calculate the specific heat of the substance using the provided formula.

Precautions

• Ensure accurate measurements of mass and temperature.
• Use polystyrene cups with negligible heat capacity.
• Stir the water thoroughly to ensure uniform temperature distribution.
• Handle hot water with care to avoid burns.
• Repeat the experiment to ensure the reliability of results.

Short Questions with Answers

1. What is specific heat?
   Answer: Specific heat is the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius.
2. How is the specific heat of a substance determined in this experiment?
   Answer: By using the method of mixture with known quantities of hot and cold water.
3. Why are polystyrene cups used as containers?
   Answer: Polystyrene cups have negligible heat capacity, minimizing heat loss to the surroundings.
4. What is the purpose of measuring the initial temperatures of hot and cold water?
   Answer: To calculate the temperature change of the water mixture.
5. Why is it important to stir the water thoroughly before measuring the final temperature?
   Answer: To ensure uniform temperature distribution in the mixture.
6. What factors affect the accuracy of the experiment?
   Answer: Accurate measurements of mass and temperature, and proper mixing of water.
7. How does the specific heat of water affect the final temperature of the mixture?
   Answer: Water with higher specific heat will result in a smaller temperature change in the mixture.
8. What happens to the heat lost by the hot water in the mixture?
   Answer: It is absorbed by the cold water and the surroundings.
9. What is the purpose of repeating the experiment?
   Answer: To ensure the reliability and consistency of the results.
10. What is the role of the polystyrene cups in the experiment?
    Answer: They act as containers with negligible heat capacity.
11. Why is it important to record the masses of the cups with water?
    Answer: To ensure accurate measurements of mass and calculate the heat absorbed by the cups.
12. What is the expected final temperature of the mixture?
    Answer: It should be between the initial temperatures of hot and cold water.
13. What precautions should be taken when handling hot water?
    Answer: Handle with care to avoid burns.
14. What is the SI unit of specific heat?
    Answer: Joule per kilogram per Celsius (J/kg°C).
15. What is the relationship between specific heat and temperature change?
    Answer: Higher specific heat results in smaller temperature changes for the same amount of heat.
16. How does the mass of water affect the temperature change of the mixture?
    Answer: A greater mass of water results in a smaller temperature change for the same amount of heat.
17. What happens if the water is not mixed properly before measuring the final temperature?
    Answer: The temperature reading may not represent the true equilibrium temperature of the mixture.
18. Why are the cups made of polystyrene rather than metal?
    Answer: Polystyrene has negligible heat capacity, minimizing heat loss to the surroundings.
19. What role does the specific heat of water play in everyday life?
    Answer: It helps regulate temperature changes in oceans, lakes, and human bodies.
20. What is the significance of measuring the initial and final temperatures?
    Answer: It allows calculation of the temperature change and determination of specific heat.

Multiple-Choice Questions (MCQs)

1. What is the purpose of using polystyrene cups in this experiment?
   A) To increase heat transfer
   B) To decrease heat transfer
   C) To minimize heat capacity
   D) To maximize heat absorption
   Correct Answer: C) To minimize heat capacity
2. How does the final temperature of the mixture compare to the initial temperatures of hot and cold water?
   A) It is always higher than both
   B) It is always lower than both
   C) It is the average of both
   D) It depends on the specific heat of the substances
   Correct Answer: C) It is the average of both
3. What happens to the heat lost by the hot water?
   A) It is absorbed by the cold water
   B) It is transferred to the surroundings
   C) It is converted into mechanical energy
   D) It remains constant
   Correct Answer: A) It is absorbed by the cold water
4. Why is it important to measure the mass of the cups with water?
   A) To calculate the heat capacity of the cups
   B) To determine the specific heat of water
   C) To ensure accurate measurements of mass
   D) To calculate the heat lost to the surroundings
   Correct Answer: C) To ensure accurate measurements of mass
5. What is the SI unit of specific heat?
   A) Joule (J)
   B) Joule per kilogram (J/kg)
   C) Joule per gram per Celsius (J/g°C)
   D) Joule per kilogram per Celsius (J/kg°C)
   Correct Answer: D) Joule per kilogram per Celsius (J/kg°C)