When gasoline is burned, it releases 1.3E8 J of energy per gallon (3.788 L). a.

Question

When gasoline is burned, it releases 1.3E8 J of energy per gallon (3.788 L).
a. Given that the density of gasoline is 737kg/m3, express the quantity of energy released in of fuel.
b. During fission, when a neutron is absorbed by a 235U nucleus, about 200 MeV of energy is released for each nucleus thatundergoes fission. Express this quantity in J/g of fuel.
c. In the proton-proton chain that takes placein stars like our sun, the overall fusion reaction can be summarized as six protons fusing to form one nucleus with two leftover protons and the liberation of 26.7 MeV of energy. The fuel is the six protons. Express the energy produced here in units of J/g of fuel.
d. Our sun produces energy at a measured rate of 3.86E26. If its mass of 1.99E30kg were all gasoline, how long could it last before consuming all its fuel?

Explanation / Answer

a. 1.3 x 108 J/gallon is equal to 3.43 x 107 J/liter. At 737 kg/m3, this is 2.53 x 1010 J/g.

b. A U235 nucleus is 235/(6.02 x 1023) = 3.9 x 10-22 g, and since a Joule is equal to a coulomb-volt, 200 MeV is (2 X 108)(1.602 x 10-19) = 3.2 x 10-11 J. The energy density is thus (3.2 x 10-11)/(3.9 x 10-22) = 8.21 x 1010 J/g.

c. Since 4 protons are consumed, the reaction burns 4/(6.02 x 1023) = 6.64 x 10-24 g, and produces (2.67 x 107)(1.602 x 10-19) = 4.28 x 10-12 J. The energy density for the proton-proton chain is thus (4.28 x 10-12)/(6.64 x 10-24) = 6.44 x 1011) J/g.

d. 1.99 x 1030 kg x 2.53 x1013 J/kg = 5.03 x 1043 J. Assuming an unlimited supply of oxygen, The sun would last 5.03 x 1043 / 3.86 x 1026 = 1.30 x 1017 seconds, divided by 3600 seconds in an hour, 24 hours in a day, and 365.25 days in a year, is 4.13 billion years. We wouln't be here.

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