Q41P - Fundamentals Of Physics

Question

A 120 V potential 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?

Step-by-Step Solution

Answer

1. The rate of transfer of the electrical energy to thermal energy is 1.0 kW.
2. The cost of this energy transfer for 5h at US $0.05/kw.h is US $0.25.

Step 1: The given data

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 is US $0.05/kw.h

Step 2: Understanding the concept of rate of energy transfer

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)

Step 3: (a) Calculation of the rate of the energy transfer

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.

Step 4: (b) Calculation of the cost value

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 $US \$0.25$.