Chapter 16, Problem 45A

A 100-watt light bulb consumes 100 joules of energy every second. How long could you burn that light bulb from the energy in one penny, which has a mass of 0.003 kg? (Assume all the penny’s mass is converted to energy.)

To determine

Duration that the light bulb will burn from the energy in penny.

Answer to Problem 45A

The light bulb can burn for $t=2.7\times {10}^{12}\text{s}=\text{85616 years approx}$ .

Explanation of Solution

Given:

Mass of one penny is, $m=0.003\text{kg}$

Power of bulb, $P=100\text{W}$

Formula Used:

From Einstein energy mass relation, the energy is given as $E=m{c}^2$

Where, $m$ is the mass and $c$ is velocity of light.

Calculation:

As, velocity of light is $c=3\times {10}^8\text{m/s}$

So, from energy-mass relation the energy in penny is

  $\begin{array}{l}E=0.003\times {\left(3\times {10}^8\right)}^2\\ =2.7\times {10}^{14}\text{J}\end{array}$

Now, energy consumed by bulb is 100 J per second.

So, duration for which light bulb burn is

  $\begin{array}{c}t=\frac{2.7\times {10}^{14}}{100}\\ =2.7\times {10}^{12}\text{s}\\ \text{=}\text{85616 years approx}\end{array}$

Conclusion:

Therefore, the light bulb can burn for $t=2.7\times {10}^{12}\text{s}=\text{85616 years approx}$ .