Final answer:
The energy required to maintain an indoor temperature is proportional to the temperature difference from the outside. More energy is needed to keep the inside at 22°C compared to 13°C when the outside temperature is 10°C, due to the greater temperature difference and resultant higher rate of heat loss.
Step-by-step explanation:
When considering how much energy must be expended to maintain different temperatures within a space, one must understand that the energy required is directly proportional to the temperature difference between the inside and outside. If the outside temperature is steady at 10°C and you want to keep the inside at a comfortable 22°C, which is often viewed as a shorts-and-short-sleeves indoor temperature, you'll need to expend more energy compared to a situation where the inside is maintained at a dress-more-warmly temperature of 13°C. The energy required increases because the thermal gradient—or temperature difference—is greater.
This concept is based on the principle that heat flows from warmer to cooler areas, and maintaining a higher temperature difference requires more work to continuously replace the heat lost to the outside environment. The rate of heat radiation is also influenced by the temperature difference; a body at 40°C radiates heat at a higher rate than when it is at 20°C. Understanding these principles of thermodynamics is essential for calculating the energy needs for heating or cooling a space.