Chapter 13, Problem 80GP

To determine

To Find: The temperature.

Answer to Problem 80GP

The temperature at which the molecules striking the nose of the vehicle is $1.4\times {10}^5\text{ K}$ .

Explanation of Solution

Given:

Velocity $v_{rms}=11111\text{ m/s}$

Atomic mass of nitrogen $m=28\times 1.66\times {10}^{-27}\text{ kg }=4.648\times {10}^{-26}\text{ kg}$ .

Boltzmann constant $\mathrm{k}=1.38\times {10}^{-23}\text{ J/K}$ .

Formula used:

Write the expression for root mean square velocity.

  $v_{rms}=\sqrt{\frac{3kT}{m}}$

Here,

  $k$ is boltzmann constant,

  $T$ is temperature in $\text{K}$ ,

  $m$ is mass of molecule.

It can be written as

  $T=v_{rms}{}^2\times \frac{m}{3\times k}$

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}\text{rms speed},v_{rms}=\sqrt{\frac{3kT}{m}}\\ T=v_{rms}{}^2\times \frac{m}{3k}\\ T={\left(11111\right)}^2\times \frac{4.648\times {10}^{-26}}{3\times 1.38\times {10}^{-23}}=1.4\times {10}^5\text{ K}\end{array}$

Conclusion:

Thus, the temperature at which the molecules striking the nose of the vehicle is $1.4\times {10}^5\text{ K}$ .