Q63PE - College Physics (Urone)

Question

(a) Using data from Table \(7.1\), find the mass destroyed when the energy in a barrel of crude oil is released. 

(b) Given these barrels contain \(200\) litres and assuming the density of crude oil is\(750{\rm{ }}kg/{m^3}\), what is the ratio of mass destroyed to original mass, \(\Delta m/m\)?

Step-by-Step Solution

Answer

a. The mass destroyed is obtained as: \(6.5{\rm{ }}\times{\rm{ }}{10^{ - 8}}{\rm{ }}kg\).

b. The ratio of the mass destroyed to original mass is obtained as:\(4.4{\rm{ }}\times{\rm{ }}{10^{ - 10}}\).

Step 1: Given Data

Quantity of crude oil is:

\(200litres\)

Density of crude oil is:\(750kg/{m^3}\).

Step 2: Define Relativity

Regarding the nature and behaviour of light, space, time, and gravity, relativity is the idea that different physical events rely on the relative motion of the observer and the observed objects.

Step 3: Evaluating the mass destroyed

a. The energy of one barrel of oil is:

\(E{\rm{ }} = {\rm{ }}5.9{\rm{ }} \times {\rm{ }}{10^9}{\rm{ }}J\).

The speed of light is:\(c{\rm{ }} = {\rm{  }}3{\rm{ }}\times{\rm{ }}{10^8}{\rm{ }}m/s\).

So, the mass destroyed is obtained as:

\(\begin{aligned}\Delta m{\rm{ }} = {\rm{ }}\dfrac{E}{{{c^2}}}\\ = \dfrac{{5.9{\rm{ }} \times {\rm{ }}{{10}^9}{\rm{ }}J}}{{{{(3{\rm{ }}\times{\rm{ }}{{10}^8}{\rm{ }}m/s)}^2}}}\\ = 6.5{\rm{ }}\times{\rm{ }}{10^{ - 8}}{\rm{ }}kg\end{aligned}\)

Therefore, the mass destroyed is:\(6.5{\rm{ }}\times{\rm{ }}{10^{ - 8}}{\rm{ }}kg\).

Step 4: Evaluating the ratio of mass destroyed to original mass

b. The values we have:

 

So, the mass obtained is:

 

The ration then will be:

\(\begin{aligned}\dfrac{{\Delta m}}{m} = \dfrac{{6.5{\rm{ }}\times{\rm{ }}{{10}^{ - 8}}{\rm{ }}kg}}{{150kg}}\\ = 4.4{\rm{ }}\times{\rm{ }}{10^{ - 10}}\end{aligned}\)

Therefore, the ratio is: \(4.4{\rm{ }}\times{\rm{ }}{10^{ - 10}}\).