Question

Conduct this experiment to determine the heat loss coefficient of your house or apartment in \(\mathrm{W} /{ }^{\circ} \mathrm{C}\) or $\mathrm{Btu} / \mathrm{h} \cdot{ }^{\circ} \mathrm{F}$. First make sure that the conditions in the house are steady and the house is at the set temperature of the thermostat. Use an outdoor thermometer to monitor outdoor temperature. One evening, using a watch or timer, determine how long the heater was on during a \(3-h\) period and the average outdoor temperature during that period. Then using the heat output rating of your heater, determine the amount of heat supplied. Also, estimate the amount of heat generation in the house during that period by noting the number of people, the total wattage of lights that were on, and the heat generated by the appliances and equipment. Using that information, calculate the average rate of heat loss from the house and the heat loss coefficient.

Short answer

Question: Calculate the heat loss coefficient of a house using the heater's runtime, heat output rating, thermostat setting, average outdoor temperature, number of people, wattage of lights, and heat generated by appliances and equipment during a 3-hour period.

Step-by-step solution

Determine the heater's runtime

Measure the time during the 3-hour period that the heater is on using a watch or timer.

Calculate total heat supplied by the heater

Multiply the heater's runtime (in hours) with its heat output rating to obtain the total amount of heat supplied by the heater during that period. \(\mathrm{Heat \thinspace supplied} = \mathrm{Runtime} \times \mathrm{Heat \thinspace output \thinspace rating}\)

Estimate the heat generated inside the house

Estimate the heat generation during the given period by taking into account: - The number of people: Assign a value of about \(100\,\mathrm{W}\) per person as the average heat generated by a seated person - The total wattage of lights that were on - The heat generated by the appliances and equipment used: Check the wattage of these items on their label or user's manual Add these values to get the total heat generation in the house.

Calculate the average rate of heat loss

Subtract the total heat generated inside the house from the total heat supplied by the heater. Divide this value by 3 hours to find the average rate of heat loss during this period. \(\mathrm{Average \thinspace rate \thinspace of \thinspace heat \thinspace loss} = \frac{\mathrm{Total \thinspace heat \thinspace supplied \thinspace by \thinspace heater} - \mathrm{Total \thinspace heat \thinspace generated \thinspace inside \thinspace house}}{3\,\mathrm{hours}}\)

Calculate the heat loss coefficient

Divide the average rate of heat loss by the difference between the indoor temperature (thermostat setting) and the average outdoor temperature during the 3-hour period to find the heat loss coefficient. \(\mathrm{Heat \thinspace loss \thinspace coefficient} = \frac{\mathrm{Average \thinspace rate \thinspace of \thinspace heat \thinspace loss}}{\mathrm{Indoor \thinspace temperature} - \mathrm{Average \thinspace outdoor \thinspace temperature}}\)Express the heat loss coefficient in \(\mathrm{W}/{ }^{\circ}\mathrm{C}\) or \(\mathrm{Btu}/\mathrm{h}\cdot{ }^{\circ}\mathrm{F}\).