**Problem Description**At what temperature would the rms (root mean square) speed of hydrogen atoms equal the following speeds? (Note: The mass of a hydrogen atom is \(1.66 \times 10^{-27}\) kg.)**Questions**(a) The escape speed from Earth, \(1.12 \times 10^4\) m/s \[ \boxed{\phantom{K}} \] K(b) The escape speed from the Moon, \(2.37 \times 10^3\) m/s \[ \boxed{\phantom{K}} \] K---The above content presents a physics problem that seeks to find the temperature at which the root mean square (rms) speed of hydrogen atoms would equal the given escape speeds from Earth and the Moon. The mass of a hydrogen atom is provided, which is \(1.66 \times 10^{-27}\) kg. Students are expected to calculate the temperatures for the hydrogen atoms' rms speeds to match specified velocities.**Scientific Background**This exercise involves concepts from thermodynamics and kinetic theory of gases, where the rms speed of gas particles can be linked to temperature using the formula:\[ v_{rms} = \sqrt{\frac{3k_BT}{m}} \]Where:- \( v_{rms} \) is the root mean square speed of the gas particles.- \( k_B \) is Boltzmann's constant (\(1.38 \times 10^{-23}\) J/K).- \( T \) is the temperature in Kelvins.- \( m \) is the mass of a single gas particle.By rearranging this formula to solve for temperature, \( T \), we get:\[ T = \frac{m v_{rms}^2}{3 k_B} \]Students will use this formula to find the required temperatures for the helium atoms' rms speeds to match the escape speeds from Earth and Moon.**Instructions for Students**1. Use the provided formula to solve for temperature: \[ T = \frac{m v_{rms}^2}{3 k_B} \] 2. Substitute the given values for \( m \), \( v_{rms} \), and \( k_B \) to find the temperatures.3. Make sure to convert the escape speeds provided in m/s correctly within your calculations.4. Insert your final

Given:mass of hydrogen, mH = 1.66×10-27 kgearth escape speed = 1.12×104 m/sescape speed moon =…

At what temperature would the rms speed of hydrogen atoms equal the following speeds? (Note: The mass of a hydrogen atom is 1.66 x 10-27 kg.) (a) the escape speed from Earth, 1.12 x 104 m/s K (b) the escape speed from the Moon, 2.37 x 10³ m/s K

At what temperature would the rms speed of hydrogen atoms equal the following speeds? (Note: The mass of a hydrogen atom is 1.66 x 10-27 kg.) (a) the escape speed from Earth, 1.12 x 104 m/s K (b) the escape speed from the Moon, 2.37 x 10³ m/s K

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Kinetic Theory of Gas

The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.

P-V Diagram

A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.

Question

**Problem Description**

At what temperature would the rms (root mean square) speed of hydrogen atoms equal the following speeds? (Note: The mass of a hydrogen atom is \(1.66 \times 10^{-27}\) kg.)

**Questions**

(a) The escape speed from Earth, \(1.12 \times 10^4\) m/s
\[ \boxed{\phantom{K}} \] K

(b) The escape speed from the Moon, \(2.37 \times 10^3\) m/s
\[ \boxed{\phantom{K}} \] K

---

The above content presents a physics problem that seeks to find the temperature at which the root mean square (rms) speed of hydrogen atoms would equal the given escape speeds from Earth and the Moon. The mass of a hydrogen atom is provided, which is \(1.66 \times 10^{-27}\) kg. Students are expected to calculate the temperatures for the hydrogen atoms' rms speeds to match specified velocities.

**Scientific Background**

This exercise involves concepts from thermodynamics and kinetic theory of gases, where the rms speed of gas particles can be linked to temperature using the formula:
\[ v_{rms} = \sqrt{\frac{3k_BT}{m}} \]

Where:
- \( v_{rms} \) is the root mean square speed of the gas particles.
- \( k_B \) is Boltzmann's constant (\(1.38 \times 10^{-23}\) J/K).
- \( T \) is the temperature in Kelvins.
- \( m \) is the mass of a single gas particle.

By rearranging this formula to solve for temperature, \( T \), we get:
\[ T = \frac{m v_{rms}^2}{3 k_B} \]

Students will use this formula to find the required temperatures for the helium atoms' rms speeds to match the escape speeds from Earth and Moon.

**Instructions for Students**

1. Use the provided formula to solve for temperature:
\[ T = \frac{m v_{rms}^2}{3 k_B} \]

2. Substitute the given values for \( m \), \( v_{rms} \), and \( k_B \) to find the temperatures.

3. Make sure to convert the escape speeds provided in m/s correctly within your calculations.

4. Insert your final

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