Question

The amount of heat required to maintain a constant temperature in the apartment is 13 MJ per hour. For how many hours is enough heat released by heating 20 kg of wood enough to maintain a constant room temperature if half of the heat obtained would go to heating the room?

A. 26 hours
B. 39 hours
C. 52 hours
D. 65 hours

Answer 1

The wood will release enough heat to maintain a constant room temperature for approximately 2.03 minutes.

Step-by-step explanation:

In order to determine how many hours the heat released by heating 20 kg of wood is enough to maintain a constant room temperature, we need to calculate the amount of heat released by the wood and then divide it by the amount of heat required per hour to maintain the temperature.

1. First, we need to find the total heat released by the wood. Since half of the heat obtained goes to heating the room, we only consider half of the heat.
2. To find the heat released, we use the formula: heat released = mass × specific heat capacity × change in temperature.
3. Given that the specific heat capacity of wood is approximately 2.2 J/g°C, we can calculate the heat released as follows: heat released = 20 kg × 2.2 J/g°C × 00°C = 440 J.
4. Now, we divide the heat released by the amount of heat required per hour to maintain the temperature. Since 1 MJ (megajoule) = 1,000,000 J, we have: hours = heat released ÷ heat required per hour = 440 J ÷ (13 MJ/hr × 1,000,000 J/MJ) = 0.033846 hours.

To convert this to minutes, we multiply the value by 60: minutes = 0.033846 hours × 60 minutes/hour ≈ 2.03 minutes.

Therefore, the wood will release enough heat to maintain a constant room temperature for approximately 2.03 minutes.