Question

1500-W heater is connected to a 120-V line for 2.0 hours.How much heat energy is produced?

A) 1.5 kJ B) 11 MJ C) 0.18 MJ D) 3.0 kJ

Answer 1

Concepts and reason

The concept required to solve this problem is the relation between the power, heat consumed, time for which the heater works.

First, Convert the hours to seconds for which the heater works.

Then, multiply the time to power to get the value of heat energy produced by the heater.

Fundamentals

The relation between the power required by the heater and heat produced by the heater is given as follows:

$Q = Pt$

Here, Q is the heat produced by the heater, P is the power consumed by the heater, and t is the time for which heater runs.

Calculate the time for which the heater works in seconds is given as follows:

$\begin{array}{c}\\t = \left( {2.0{\rm{ hours}}} \right)\left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ hour}}}}} \right)\\\\ = 7200{\rm{ s}}\\\end{array}$

Therefore, the heater works for 7200 s.

Calculate the heat energy produced by the heater as follows:

$Q = Pt$

Substitute 1500 W for P and 7200 s for t in the above-mentioned equation.

$\begin{array}{c}\\Q = \left( {1500{\rm{ W}}} \right)\left( {7200{\rm{ s}}} \right)\left( {\frac{{{\rm{J}} \cdot {{\rm{s}}^{ - 1}}}}{{1{\rm{ W}}}}} \right)\\\\ = \left( {10.8 \times {{10}^6}{\rm{ J}}} \right)\left( {\frac{{{{10}^{ - 6}}{\rm{ MJ}}}}{{1{\rm{ J}}}}} \right)\\\\ = 10.8{\rm{ MJ}}\\\\ \approx 11{\rm{ MJ}}\\\end{array}$

Therefore, correct answer is option-B) 11 MJ.

Ans:

The correct answer is option-B) 11 MJ.