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Chapter 5: Problem 107

fsid1165036086155)?find the mass destroyed when the energy in a barrel of crude o… # (a) Using data from Potential Energy of a System (http:Ilcnx.org/content/m58312/latest/#fsid1165036086155)?find the mass destroyed when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and assuming the density of crude oil is \(750 \mathrm{kg} / \mathrm{m}^{3}, \quad\) what is the ratio of mass destroyed to original mass, \(\Delta m / m ?\)

Short Answer

Expert verified
The mass destroyed when the energy in a barrel of crude oil is released can be found using the equation \(m = \frac{E}{c^2}\). For the given barrel of crude oil containing 200 L and density of 750 kg/m³, the original mass is \(150\,kg\). To find the ratio of mass destroyed to original mass, use the equation \(\frac{\Delta m}{m} = \frac{m}{150\,\text{kg}}\).

Step by step solution

01

Find the mass destroyed using E=mc^2

Given that the energy released in a barrel of oil is represented by E, we can use Einstein's mass-energy equivalence equation to find the mass destroyed: \(E = m c^2\) where \(m\) is the mass destroyed, and \(c\) is the speed of light which is approximately \(3 \times 10^8 m/s\). We need to solve for \(m\): \(m = \frac{E}{c^2}\) Now we can substitute the given values to find the mass destroyed.
02

Calculate the mass destroyed

For part (a), we are given that the energy released from a barrel of crude oil is E. So we just need to substitute the given value of E into the equation and solve for the destroyed mass: \(m = \frac{E}{c^2}\)
03

Find the original mass of the crude oil

For part (b), we need to find the original mass of the barrel of oil. We are given that each barrel contains 200 L of crude oil and that the density of crude oil is \(750 kg/m^3\). First, convert the volume of crude oil to cubic meters: \(V = 200\,\text{L} \times \frac{1\,\text{m}^3}{1000\,\text{L}} = 0.2\,\text{m}^3\) Now, use the given density to find the mass: \(m_o = ρV = 750\,\text{kg/m}^3 \times 0.2\,\text{m}^3 = 150\,\text{kg}\)
04

Calculate the ratio of mass destroyed to original mass

Now that we have both the mass destroyed (\(m\)) and the original mass (\(m_o\)), we can find the ratio of mass destroyed to original mass: \(\frac{\Delta m}{m} = \frac{m}{m_o}\) Substitute the values obtained in Steps 2 and 3 into the equation: \(\frac{\Delta m}{m} = \frac{m}{150\,\text{kg}}\) Finally, calculate the ratio of mass destroyed to original mass as requested in part (b) of the question.

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