A $1500-W$ electric heater is connected to a $120-V$ power line. How much heat energy, in joules, does it produce in $2.0$ hours of operation?

• A. $9.00\times {10}^7$ joules
• B. $3.60\times {10}^6$ joules
• C. $2.50\times {10}^5$ joules
• D. $1.08\times {10}^7$ joules

Answer: (D)

Verified step by step guidance

1. Identify the given quantities: power of the heater \(P = 1500\ \text{W}\), voltage \(V = 120\ \text{V}\) (though voltage is not directly needed here), and time of operation \(t = 2.0\ \text{hours}\).
2. Convert the time from hours to seconds because power is in watts (joules per second). Use the conversion \$1\ \text{hour} = 3600\ \text{seconds}\(, so \)t = 2.0 \times 3600\ \text{seconds}$.
3. Recall the relationship between power, energy, and time: power is the rate of energy transfer, so energy produced \(Q\) is given by the formula \(Q = P \times t\).
4. Substitute the known values into the formula: multiply the power \$1500\ \text{W}$ by the time in seconds to find the total heat energy produced in joules.
5. Express the final answer in scientific notation to match the format of the options given.