Final answer:
For a house with a heat loss rate of 200 W/°C, equipped with two 1,500 W heaters, the coldest outdoor temperature it can handle while maintaining a 20°C indoor temperature is 5°C. This is calculated based on the heaters' combined maximum output and the heat loss rate of the house.
Step-by-step explanation:
Understanding House Thermal Dynamics
When considering the heat requirements for maintaining a comfortable indoor temperature, it's important to understand the relationship between a house's heat loss rate and the capacity of its heater. For a house with a heat loss rate of 200 W/°C and equipped with two 1,500 W space heaters, we can calculate the coldest outdoor temperature it can handle whilst still maintaining an internal temperature of 20°C. The combined output of the space heaters is 3,000 W (2x1,500 W).
The power required to maintain a 20°C difference between the indoor and outdoor temperatures is given by the product of the heat loss rate and the temperature difference (ΔT). In this case, that would be 200 W/°C times 20°C, resulting in 4,000 W.
Since the heaters can only provide 3,000 W, they are incapable of sustaining a 20°C difference when the heat loss at that difference would be 4,000 W. To find the maximum ΔT these heaters can maintain, we divide the total heating power by the heat loss rate: 3,000 W divided by 200 W/°C, resulting in a maximum ΔT of 15°C. This means the coldest it can get outside while maintaining an internal temperature of 20°C is 5°C (20°C - 15°C).