Chapter 13, Problem 65A

Interpretation Introduction

Interpretation:

The temperature at the center of the sun is to be determined on the bases of the given information.

Concept introduction:

The ideal gases are those gases which obey the ideal gas equation and the ideal gas equation is written as

  $\text{PV}\text{= nRT}$

Answer to Problem 65A

The temperature at the center of the sun is

Explanation of Solution

Given information:

Average molar mass = 2

Pressure = $\begin{array}{l}\text{1}{\text{.3×10}}^{\text{9}}\text{atm}\\ \end{array}$

Density = $\text{1}\text{.4}{\text{g/cm}}^{\text{3}}$

Gas constant = $\text{82}\text{.05745 }{\text{cm}}^{\text{3}}\text{atm}\text{}\text{}{\text{K}}^{\text{-1}}\text{}{\text{mol}}^{\text{-1}}$

Calculation:

According to the ideal gas equation

  $\begin{array}{l}\text{T}\text{=}\frac{\text{PV}}{\text{nR}}\\ \end{array}$

Number of moles,

  $\begin{array}{l}\text{n=}\frac{\text{m}}{\text{V}}\\ \text{V}\text{=}\frac{\text{m}}{\text{n}}\end{array}$

Put the value of V in abode equation, we get

  $\begin{array}{l}\text{T=}\frac{\text{P×m}}{\text{n×P×R}}\\ \text{=}\frac{{\text{P×M}}_{\text{w}}\text{×}\text{n}}{\text{n×ρ×R}}\left({\text{M}}_{\text{w}}\text{=}\frac{\text{molar}\text{mass}}{\text{number}\text{of}\text{moles}}\right)\\ \text{=}\frac{{\text{P×M}}_{\text{w}}}{\text{ρ×R}}\\ \text{=}\frac{\text{1}{\text{.3×10}}^{\text{9}}\text{×2}}{\text{1}\text{.4×82}\text{.05}}\\ \text{=}\text{0}{\text{.022×10}}^{\text{9}}\text{K}\end{array}$

Conclusion

The temperature at the centre of sun under given conditions is $\text{0}{\text{.022×10}}^{\text{9}}\text{K}$ .