The energy given off by a spherical star, such as our sun, is equal to \(\sigma A T^4\), where \(\sigma\) is a constant, A is the surface area of the star, and T is its temperature. Spherical star JZ114 has ten times the radius and half the temperature of our sun. What is the ratio of the energy JZ114 gives off to the energy our sun gives off? Express your answer as a common fraction.
If we consider the surface area of our Sun =1, and its temperature =1 so that the energy release =AT^4 =1*1^4 =1
If we consider the surface area of JZ114 =its radius^2 =10^2 =100 times the surface area of our Sun. And its temperature is only 1/2 of the temperature of our Sun, =1/2^4 =1/16 temperature of our Sun. Then the total energy release by JZ114 =AT^4 =100 * 1/16 =6.25 times the energy release by our Sun.
Therefore, the ratio of energy release by our Sun to that of JZ114 = 1 / 6.25