Question

Conduct the following experiment at home to determine the combined convection and radiation heat transfer coefficient at the surface of an apple exposed to the room air. You will need two thermometers and a clock. First, weigh the apple and measure its diameter. You can measure its volume by placing it in a large measuring cup halfway filled with water, and measuring the change in volume when it is completely immersed in the water. Refrigerate the apple overnight so that it is at a uniform temperature in the morning, and measure the air temperature in the kitchen. Then take the apple out and stick one of the thermometers to its middle and the other just under the skin. Record both temperatures every \(5 \mathrm{~min}\) for an hour. Using these two temperatures, calculate the heat transfer coefficient for each interval and take their average. The result is the combined convection and radiation heat transfer coefficient for this heat transfer process. Using your experimental data, also calculate the thermal conductivity and thermal diffusivity of the apple and compare them to the values given above.

Short answer

Answer: The steps to perform the experiment are as follows: 1. Gather materials and collect initial data by measuring the apple's weight, diameter, and volume. 2. Refrigerate the apple overnight for uniform temperature and measure the air temperature in the experiment room. 3. Take temperature measurements of the apple's core and surface every 5 minutes for an hour. 4. Calculate the heat transfer coefficient for each time interval using Fourier's Law and Newton's Law of Cooling. 5. Calculate the average heat transfer coefficient over the entire process. 6. Use the average heat transfer coefficient and recorded temperatures to calculate the thermal conductivity and thermal diffusivity of the apple. 7. Compare the calculated values with the given values to verify the accuracy of the experiment.

Step-by-step solution

Gather Materials and Collect Initial Data

Prepare two thermometers, a clock, a weighing scale, and a measuring cup. Weigh the apple and measure its diameter. Immerse the apple in a measuring cup half-filled with water and measure the change in volume to determine the apple's volume.

Prepare the Apple

Refrigerate the apple overnight to ensure it has a uniform temperature. Measure the air temperature in the room where the experiment will take place.

Take Temperature Measurements

Remove the apple from the refrigerator. Insert one thermometer in the middle of the apple and the other just under the skin. Record the temperatures of both thermometers every 5 minutes for an hour.

Calculate Heat Transfer Coefficient for Each Interval

Using the recorded temperatures and the apple's geometry, calculate the heat transfer coefficient for each time interval using Fourier's Law and Newton's Law of Cooling.

Calculate Average Heat Transfer Coefficient

Take the average of the calculated heat transfer coefficients to determine the combined convection and radiation heat transfer coefficient for the entire process.

Calculate Thermal Conductivity and Thermal Diffusivity

Use the average heat transfer coefficient and the recorded temperatures to calculate the thermal conductivity and thermal diffusivity of the apple.

Compare Calculated Values with Given Data

Compare the calculated values for thermal conductivity and thermal diffusivity with the given values to verify the accuracy of the experiment.