Answer
To maintain a constant temperature inside the house, the rate of heat loss must be equal to the rate of heat gain.
Let's assume that the indoor temperature is 21°C, and the outdoor temperature is T°C.
The rate of heat gain through the windows is 2.2 kW.
The rate of heat loss through the walls and windows is given by:
Rate of heat loss = (indoor-outdoor temperature difference) x (thermal conductance of the house)
Thermal conductance is the inverse of thermal resistance, and it tells us how much heat flows through a material for a given temperature difference.
Here, the thermal conductance of the house is given as 55 W/°C. So, the rate of heat loss is:
Rate of heat loss = (21 - T) x 55 W/°C
For the house to maintain a constant temperature, we need the rate of heat gain to be equal to the rate of heat loss.
2.2 kW = (21 - T) x 55 W/°C
Solving for T, we get:
T = 2.2 kW / (55 W/°C) + 21°C
T = 39.6°C
Therefore, the minimum outdoor temperature for which the house can maintain 21°C inside is 39.6°C.
Work Step by Step
To maintain a constant temperature inside the house, the rate of heat loss must be equal to the rate of heat gain.
Let's assume that the indoor temperature is 21°C, and the outdoor temperature is T°C.
The rate of heat gain through the windows is 2.2 kW.
The rate of heat loss through the walls and windows is given by:
Rate of heat loss = (indoor-outdoor temperature difference) x (thermal conductance of the house)
Thermal conductance is the inverse of thermal resistance, and it tells us how much heat flows through a material for a given temperature difference.
Here, the thermal conductance of the house is given as 55 W/°C. So, the rate of heat loss is:
Rate of heat loss = (21 - T) x 55 W/°C
For the house to maintain a constant temperature, we need the rate of heat gain to be equal to the rate of heat loss.
2.2 kW = (21 - T) x 55 W/°C
Solving for T, we get:
T = 2.2 kW / (55 W/°C) + 21°C
T = 39.6°C
Therefore, the minimum outdoor temperature for which the house can maintain 21°C inside is 39.6°C.
