1. Determine the coefficient of thermal conductivity of good condensation

The coefficient of thermal conductivity (often denoted by (k) or (\lambda)) refers to how efficiently a material conducts heat. For “good condensation,” if you’re referring to thermal conductivity during the process of film condensation—which occurs when vapor condenses on a cooler surface and forms a thin liquid film—then the heat transfer depends on the properties of the condensate layer and the material involved.

Here are some useful points:

1. Condensate Layer Thermal Conductivity:

• In condensation processes, materials such as water or refrigerants form the film, and water has a thermal conductivity of approximately 0.6 W/m·K at room temperature.
• This thin film acts as a thermal resistance, impacting overall heat transfer.

1. Surface Materials for Good Condensation:

• Metals like copper and aluminum are commonly used as condensation surfaces because they have high thermal conductivity (copper: ~400 W/m·K, aluminum: ~205 W/m·K).

1. Overall Coefficient in Practical Systems:

• The heat transfer coefficient ((h)) in condensation includes contributions from both film thermal resistance and surface conductivity. For film condensation on vertical walls, the typical heat transfer coefficient ranges between 1000-10,000 W/m²·K, depending on the vapor type, surface material, and condensation dynamics.

To accurately determine the thermal conductivity in a condensation scenario, you’d need to know the specific material involved, temperature, and system conditions. Are you looking for the thermal conductivity of the condensate film (like water) or of the surface facilitating condensation?

2. Determine the mechanical equivalent of heat with the help of Joules calorimeter

---

Joule’s Calorimeter Experiment to Determine Mechanical Equivalent of Heat

The mechanical equivalent of heat establishes the relationship between mechanical work and heat energy. Joule determined this experimentally using Joule’s calorimeter.

---

Apparatus Setup

1. Calorimeter: A thermally insulated container filled with water.
2. Stirrer: Rotates inside the water to generate heat.
3. Weights and Pulleys: Weights connected to a rope wound around a drum attached to the stirrer.
4. Thermometer: To measure the water’s temperature rise.

---

Procedure

1. Initial Measurements:

• Measure the mass of water (m) and the mass of the calorimeter (m_c).
• Record the initial temperature (T_1) of the water.

1. Performing Mechanical Work:

• Let the weights fall from a known height (h), rotating the stirrer inside the water.
• The potential energy of the weights is converted to heat energy, raising the water temperature.

1. Measure Final Temperature:

• After the stirring stops, record the final temperature (T_2).

---

Calculations

Mechanical Work Done (W):

W = m_w * g * h

Where:

• m_w = mass of the falling weight
• g = acceleration due to gravity (9.81 m/s²)
• h = height through which the weight falls

---

Heat Energy Gained (Q):

Q = (m * s + m_c * s_c) * (T_2 - T_1)

Where:

• m = mass of water
• s = specific heat capacity of water (4.186 J/g°C)
• m_c = mass of the calorimeter
• s_c = specific heat capacity of the calorimeter material
• T_1 = initial temperature
• T_2 = final temperature

---

Mechanical Equivalent of Heat (J):

J = W / Q

Where:

• J = mechanical equivalent of heat
• W = mechanical work done
• Q = heat energy gained

---

Conclusion

The value of the mechanical equivalent of heat (J) determined through this experiment is approximately 4.186 J/cal, meaning that 4.186 Joules of mechanical energy are required to produce 1 calorie of heat energy.

---