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Chapter 6: Q42E (page 1250)

The sun produces energy by nuclear fusion reactions, in which matter is converted into energy. By measuring the amount of energy, we receive from the sun, we know that it is producing energy at a rate of 3.8脳1026W. (a) How many kilograms of matter does the sun lose each second? Approximately how many tons of matter is this (1 ton =2000 lb )? (b) At this rate, how long would it take the sun to use up all its mass?

Short Answer

Expert verified

a)4.6脳106ton of mass sun lose each second.

b)1.49脳1013 year it takes the sun to use up all its mass.

Step by step solution

01

Define the kinetic energy and the rest energy

Kinetic energy is the difference between total energy and rest energy.

The total energyE of a particle is

E=K+mc2=mc1-v2/c2=纬mc2

Where,K is the relativistic kinetic energy. The expression ofK is:

K=mc21-v2/c2-mc2

纬is the Lorentz factor. The expression of纬 is:

纬=11-v2/c2

The energymc2 associated with rest massm rather than motion is known as rest energy of the particle.

02

Determine the mass.

Given that, total energy E=mc2.

m=Ec2=3.8脳10263脳1082脳2.2脳12000=4.6脳106ton

Hence,4.6脳106ton of mass sun lose each second.

03

Determine the time.

The mass of the sun is1.989脳1030kg

t=massrate=1.989脳10304.228脳109=1.49脳1013year

Hence, 1.49脳1013year it takes the sun to use up all its mass.

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