The core of the Sun has a temperature of 1.5 × 107 K, while the surface of the Sun has a temperature of 4870 K (which varies over the surface, with the sunspots being cooler). Treat the core of the Sun and the surface of the Sun as two large reservoirs connected by the solar interior. Nuclear fusion processes in the core produce 3.8 × 1026 J every second. Assume that 100% of this energy is transferred from the core to the surface The core of the Sun has a temperature of 1.5 × 107 K, while the surface of the Sun has a temperature of 4870 K (which varies over the surface, with the sunspots being cooler). Treat the core of the Sun and the surface of the Sun as two large reservoirs connected by the solar interior. Nuclear fusion processes in the core produce 3.8 × 1026 J every second. Assume that 100% of this energy is transferred from the core to the surface.Rigel is a blue giant star with a core temperature of 5.0 x 107 K and a surface temperature of 10100 K. If the core of Rigel produces 60,000 times as much energy per second as the core of the Sun does, calculate the change in the entropy ΔSR, in joules per kelvin, of Rigel every second.

Respuesta :

The change in entropy of the star Rigel is 22595.44×10²³J/Ks

Change in entropy:

The change in entropy of the system is given by:

[tex]\Delta S=\frac{\Delta Q}{T}[/tex]

In the case of Rigel star, the total change in entropy is given by:

[tex]\Delta S_R=\Delta S_{core}+\Delta S_{surface}[/tex]

The temperature of the core is  [tex]T_{core}=5.0 \times10^7 K[/tex]

The temperature of the surface is [tex]T_{surface}=10100 K[/tex]

Heat exchanged per second between the core and the surface is [tex]\Delta Q=2.28\times10^{31}J[/tex]

[tex]\Delta S_{core}=\frac{\Delta Q}{T_{core}}\\\\ \Delta S_{core}=\frac{-2.28\times10^{31}}{5.0\times10^7} \\\\\Delta S_{core}=-4.56\times10^{23}J/Ks[/tex]

Also,

[tex]\Delta S_{surface}=\frac{\Delta Q}{T_{surface}}\\\\ \Delta S_{surface}=\frac{2.28\times10^{31}}{10100} \\\\\Delta S_{surface}=2.26\times10^{27}J/Ks=22600\times10^{23}J/Ks[/tex]

Total change in entropy:

[tex]\Delta S_R=\Delta S_{core}+\Delta S_{surface}\\\\\Delta S_R=-4.56\times10^{23}+22600\times10^{23}\\\\\Delta S_R=22595.44\times10^{23}J/Ks[/tex]

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