Chapter 12.7, Problem 12P

To determine

To calculate: The ratio of the surface temperature, if the ratio of the heat emitted from two starts is 16:81. Also given the heat emitted from a start is directly propositional to the fourth power of the surface temperature of the star.

Answer to Problem 12P

The ratio of the surface of the temperature is $T_1^{}:T_2^{}=2:3$

Explanation of Solution

Given information:

The heat emitted from a start is directly propositional to the fourth power of the surface temperature of the star.

Let, Heat emitted in both condition are H1 and H1 and temperature of surface is T1 and T2 respectively.

So $H\prec =T^4$

Let k be a constant

  $H=k\cdot T^4$

Also given:

The amount of head emitted in first case is H1 is

  $H_1^{}=k\cdot T_1^4$....... (1)

And the amount of heat emitted in second case H2 is

  $H_2^{}=k\cdot T_2^4$...... (2)

Divide equation 1 and 2.

  $\frac{H_1^{}}{H_2^{}}=\frac{T_1^4}{T_2^4}$

Now, put the value of T1 and T2.

  $\frac{16}{81}={\left(\frac{T_1^{}}{T_2^{}}\right)}^4$

  $\frac{T_1^{}}{T_2^{}}=\sqrt{\frac{16}{81}}$

  $\frac{T_1^{}}{T_2^{}}=\frac{2}{3}$

  $T_1^{}:T_2^{}=2:3$