Question

The temperature of a room heated by a heater is 20°C when outside temperature is −20°C and it is 10°C when the outside temperature is −40°C. The temperature of the heater is:

Answer 1

The temperature of the heater is 200°C.

Step-by-step explanation:

To find the temperature of the heater, we can use the formula for power needed to maintain a specific temperature difference in a house. The formula is P = k * AT, where P is the power, k is the heat loss rate, and AT is the temperature difference between inside and outside. In this case, the power is 200 W, the inside temperature is 20°C, and the outside temperature is -20°C.

Substituting these values into the formula, we get 200 = k * (20 - (-20)). Simplifying this equation, we have 200 = k * 40. To find the value of k, we divide both sides of the equation by 40, which gives us k = 5.

Now we can use this value of k to find the temperature of the heater. If the outside temperature is -20°C, the temperature difference (AT) is 20 - (-20) = 40°C. Using the formula P = k * AT, we can substitute the values of k and AT to solve for P. Therefore, P = 5 * 40 = 200°C