The decay of 40K and other radiogenic isotopes produces 4.8 * 10-12 W/kg of heat
ID: 1350215 • Letter: T
Question
The decay of 40K and other radiogenic isotopes produces 4.8 * 10-12 W/kg of heat in Earth today.
a. If Jupiter's core is 4 Earth-masses and is made of rocky materials, what would be the total heat due to radiogenic heat generation in the core of Jupiter, assuming that the core is of similar composition to Earth? Obtain the rate in the unit of W. (Hint: Find and use the mass of Earth in order to calculate the mass of Jupiter's core.)
b. What is the surface area of Jupiter? Express it in the unit of m2. (Hint: Find and use the radius of Jupiter.)
c. Using your answers to parts a and b, calculate the heat flux of radiogenic heat generation in the core of Jupiter? Obtain the rate in the unit of W/m2.
d. Observations indicate that Jupiter generates a heat flux of about 7 W/m2 at 1 bar level. Compare this observed heat flux with the result of part c.
Explanation / Answer
Heat Produced by Radiogenic isotopes = 4.8 * 10^-12 W/kg
A.)
Mass of Jupiter core = 4* Mass of Earth
Mass of Jupiter core = 4 * 5.972 * 10^24 Kg
Mass of Jupiter core = 2.3888 * 10^25 Kg
Heat produced by Jupiter core = 4.8 * 10^-12 W/kg * 2.3888 * 10^25 Kg W
Heat produced by Jupiter core = 1.15 * 10^14 W
B)
Surface Area of Jupiter = 4*pi*R^2
Radius of Jupiter, R = 69911 * 10^3 m
Surface Area of Jupiter = 4*pi*( 69911 * 10^3 )^2
Surface Area of Jupiter = 6.142 * 10^16 m^2
C)
Heat Flux of radiogenic heat generation in the core of Jupiter = 1.15 * 10^14 W / 6.142 * 10^16 m^2
Heat Flux of radiogenic heat generation in the core of Jupiter = 1.87 * 10^-3 W/m^2
D)
1.87 * 10^-3 / 7 * 100% = 0.0267 % of Heat Flux is Produced by Jupiter core.
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