The Sun radiates energy at the rate of 3.80 ✕ 1026 W from its 5500°C surface into dark empty space (a negligible fraction radiates onto Earth and the other planets). The effective temperature of deep space is −270°C. (Due to the sensitive nature of the calculations, use T(K) = T(°C) + 273.15.(a) What is the increase in entropy (in J/K) in one day due to this heat transfer?

Respuesta :

Given:

The sun radiates energy at a rate of

[tex]W=3.80\times10^{26}\text{ W}[/tex]

The temperature in the empty space is,

[tex]\begin{gathered} T_H=5500+273 \\ =5773\text{ K} \end{gathered}[/tex]

The temperature at the deep space is,

[tex]\begin{gathered} T_c=-270+273 \\ =3\text{ K} \end{gathered}[/tex]

To find:

the increase in entropy (in J/K) in one day

Explanation:

The value of heat is,

[tex]\begin{gathered} Q_H=Q_c=Q=3.80\times10^{26}\times24\times3600 \\ =3.28\times10^{31}\text{ J} \end{gathered}[/tex]

The change in entropy is,

[tex]\begin{gathered} \Delta s=-\frac{Q_H}{T_H}+\frac{Q_c}{T_c} \\ =-\frac{3.28\times10^{31}}{5773}+\frac{3.28\times10^{31}}{3} \\ =1.08\times10^{31}\text{ J/K} \end{gathered}[/tex]

Hence, the increase in entropy is

[tex]1.08\times10^{31}\text{ J/K}[/tex]