The average thermal conductivity of the walls (including windows) and roof of a house is 4.8E-4 kW/m·°C, and their average thickness is 20.5 cm. The house is heated with natural gas, with a heat of combustion (energy given off per cubic meter of gas burned) of 9300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 27.0°C if the outside temperature is 0.0°C? Disregard radiation and energy loss by heat through the ground.I have no idea how to even go about solving this, so please show me work. THANKS!
The rate of heat transfer is given by Q = k A dT / x where k is thermal conductivity, A is the surface area, dT is the difference in temperature, and x is the thickness. If you plug in units you will see that W/m°C * m^2 °C / m gives you units of W. Hopefully from the figure you can calculate the surface area of the walls and roof. One watt is one Joule per second. One calorie is about 4.18 Joules. Use this information to find the amount of energy, in calories, that is expended over a period of 24 hours, and divide by 9,300,000 (don't forget this is in kilocalories) to find out how much gas is needed.
Average Thermal Conductivity
