A $1500$-$W$ heater is connected to a $120$-$V$ line for $2.0$ $\mathrm{hours}$. How much heat energy, in $\mathrm{joules}$, is produced by the heater during this time?

• A. $9.00\times {10}^5$ J
• B. $1.08\times {10}^7$ J
• C. $2.25\times {10}^6$ J
• D. $3.60\times {10}^6$ J

Answer: (B)

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 needed to find heat energy here), and time \(t = 2.0\ \text{hours}\).
2. Convert the time from hours to seconds because the standard unit of time in physics is seconds. Use the conversion \$1\ \text{hour} = 3600\ \text{seconds}\(, so \)t = 2.0 \times 3600\ \text{seconds}$.
3. Recall that power is the rate at which energy is transferred or converted, so the total energy (or heat energy) produced is given by the formula: \(E = P \times t\)
4. Substitute the values of power and time into the formula to express the energy in joules: \(E = 1500 \times (2.0 \times 3600)\)
5. Calculate the product to find the total heat energy produced by the heater during the 2-hour period.