Question

If the gaseous medium of the sun has pressure $1.4\times {10}^9\text{atm}$, density $1.4{\text{g cm}}^{-3}$ and average molecular weight $2\text{g/mol}$, then the temperature of the sun will be
[Given $R=8.4{\text{J mol}}^{-1}{K}^{-1}].$ Assume ideal gas behaviour.

• A. $1.2\times {10}^7\text{K}$
• B. $2.4\times {10}^7\text{K}$
• C. $0.4\times {10}^7\text{K}$
• D. $0.2\times {10}^7\text{K}$

Answer 1

The correct option is B $2.4\times {10}^7\text{K}$

Assuming the constituents of the sun follow the ideal gas law,
$PV=nRT$
where $n=\frac{m}{M}$ and $\rho =\frac{m}{V}$

$\Rightarrow T=\frac{PV}{nR}=\frac{PM}{\rho R}$
$=\frac{1.4\times {10}^9\times 1.01\times {10}^5\times 2\times {10}^{-3}}{1.4\times {10}^3\times 8.4}$
$=2.4\times {10}^7\text{K}$