A 120 Vpotential difference is applied to a space heater whose resistance is $\mathbf{14}\mathbf{}\mathbf{\Omega }$when hot. (a) At what rate is electrical energy transferred to thermal energy? (b) What is the cost for 5.0h at US $0.05/kW.h?

1. Potential difference, V = 120 V
2. Resistance of the heater,$R=14\Omega$
3. Time of transfer, t = 0.05h
4. Cost per energy isUS $0.05/kw.h

Using the concept of power, we can get the required rate of electrical energy transfer to thermal energy. Then, using this value, we can get the cost per transfer of the energy.

Formula:

The rate of energy transfer from one form to another, $P=V^2/R$ …(i)

Using the given data in equation (i), we can get the rate of transferred electrical energy to thermal energy as follows:

$\begin{array}{l}P=\frac{{\left(120V\right)}^2}{14\Omega }\\ =1.0\times {10}^{3}W\\ =1.0kW\end{array}$

Hence, the value of the rate of energy is 1.0kW.

The cost of the energy transfer using the given data can be given as follows:

$$\begin{gathered} Cost=\left(1kW\right)\left(5h\right)\left(0.05\$/kW.h\right) \\ =US\$0.25 \end{gathered}$$

Hence, the value of the required cost is $US\$0.25$.