It takes 180 MJ of energy to heat a room for 8 hours. Calculate the power of the heating element and the cost of heating the room if the cost of electricity is 26.5 cents/kWH.
Round your answers to 2 decimal places.

To calculate the power of the heating element and the cost of heating the room, we'll follow these steps:

### 1. Calculate the Power of the Heating Element
The power ($P$) can be calculated using the formula:
\[
P = \frac{E}{t}
\]
where:
- $E$ is the energy in joules (J),
- $t$ is the time in seconds (s).

Given:
- $E = 180 \, \text{MJ} = 180 \times 10^6 \, \text{J}$
- $t = 8 \, \text{hours} = 8 \times 3600 \, \text{seconds}$

Substituting the values:
\[
P = \frac{180 \times 10^6 \, \text{J}}{8 \times 3600 \, \text{s}}
\]

### 2. Calculate the Cost of Heating
The cost of heating can be calculated using the formula:
\[
\text{Cost} = P \times t \times \text{Cost per unit}
\]
Since the cost is given in $ \text{cents/kWh} $, we first need to convert the power to kilowatts (kW).

Given:
- Cost per unit = 26.5 cents/kWh
- 1 kWh = 3.6 million joules

Let's calculate both the power and the cost.### Results
1. **Power of the heating element:** $ 6.25 \, \text{kW} $
2. **Cost of heating the room for 8 hours:** 1325 cents or **$13.25**

Would you like more details on any of these calculations or have any questions?

Here are 8 related questions for further exploration:
1. How would the cost change if the electricity price increased by 10%?
2. What would be the cost for heating the room for 12 hours instead of 8?
3. How much energy in joules would be required to heat the room for 24 hours?
4. If the heating element had a power of 5 kW, how long would it take to use 180 MJ of energy?
5. What would be the power if the room required 360 MJ of energy over 8 hours?
6. How does the energy cost vary with different energy tariffs (e.g., 30 cents/kWh)?
7. What is the power in kilowatts if 150 MJ of energy is used in 6 hours?
8. How would you convert the power to horsepower?

**Tip:** When calculating power, ensure units of energy and time are consistent (e.g., joules and seconds).

Learn how to calculate the power of a heating element and the cost of heating a room using 180 MJ of energy over 8 hours. Includes step-by-step calculations with formulas for power and cost, rounding answers to 2 decimal places. Cost calculated based on electricity cost of 26.5 cents/kWh. Perfect for advanced high school students studying physics or engineering.

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