Question

Calculate the temperature of the Sun if density is $1.4gc{m^{ - 3}}$, pressure is $1.4 \times {10^9}$ atmosphere and average molecular weight of gases in the Sun in $2g/mole$. [ Given $R = 8.4Jmo{l^{ - 1}}{K^{ - 1}}$]

Answer 1

Hint: Firstly we have to figure out all the known quantities for the given question ( In this case the density, pressure and the average molecular weight). Then we can use it to interpret the missing quantity.Then we have to give the correct formula for the ideal gas law $PV = nRT$ and then use the given values to find the temperature by using it and solving it.

Complete step by step solution:
Firstly we have to sort out what we have got :
The density of the sun : $1.4gc{m^{ - 3}}$
The pressure of the sun in terms for atm : $1.4 \times {10^9}$
And, the average molecular weight of gases in the sun : $2g/mole$
Step 1: We have to define the presumed temperature by $T$ . To find that we have to use the ideal gas law as we have all other aspects for it apart from the temperature :
$PV = nRT$
Step 2: Now we just have to interpret the equation in terms of the temperature and then use the values to determine it:
$
  PV = nRT \\
  T = \dfrac{{PV}}{{nR}} \\
 $
Step 3: Now after that we have the value in the terms of T so we can get the answer.
$
\Rightarrow T = {\dfrac{{1.4 \times {{10}^3} \times {{10}^5} \times 1.4 \times 10}}{{{{({{10}^{ - 2}})}^3} \times 8.4}}^{ - 3}} \\
\Rightarrow T = 2.33 \times {10^{16}}K \\
 $
Hence the value of the temperature is $T = 2.33 \times {10^{16}}K$.

Note: The law can only be implemented when the conditions are ideal and sustainable. Apart from that it is important to use the SI units for the solving purpose. For eg;- Pascals, or Newtons of force per square meter of area. So we should do the interconversion when needed.