**Nitrogen Gas Molecules Experiment**A collection of nitrogen gas molecules is at \( P = 100,000 \, \text{Pa}, \, T = 25^\circ \, \text{C} \), and is held in a box of Volume \( V = 2 \, \text{m}^3 \). Answer all the following:(a) **How many molecules are in the box?**(b) **What is the average Translational Kinetic Energy of one of these molecules?**(c) **What is the RMS (Root Mean Square) velocity of one of these molecules?**(d) **What is the internal energy of the system?**(e) **How much heat is required to raise the temperature of the gas to \( 35^\circ \, \text{C} \) if the volume is not changed as the heat is added?**(f) **How much heat is required to raise the temperature of the gas to \( 35^\circ \, \text{C} \) if the volume is allowed to change in such a way that the pressure is not changed?**(g) **What is the change in internal energy of the gas during each of the two previous processes?**This exercise involves calculations using the ideal gas law, kinetic theory of gases, and thermodynamics, focusing on changes in energy and molecular behavior under different conditions.

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A collection of nitrogen gas molecules is at P - 100,000 Pa, T = 25° C, and is held in a box of Volume V = 2 m³. Answer all the following: (a) How many molecules are in the box? (b) What is the average Translational Kinetic Energy of one of these molecules? (c) What is the (d) What is the internal energy of the system? RMS velocity of one of these molecules? (e) How much heat is required to raise the temperature of the gas to 35⁰ C if the volume is not changed as the heat is added? (f) How much heat is required to raise the temperature of the gas to 35º C if the volume is allowed to change in such a way that the pressure is not changed? (g) What is the change in internal energy of the gas during each of the two previous processes?

A collection of nitrogen gas molecules is at P - 100,000 Pa, T = 25° C, and is held in a box of Volume V = 2 m³. Answer all the following: (a) How many molecules are in the box? (b) What is the average Translational Kinetic Energy of one of these molecules? (c) What is the (d) What is the internal energy of the system? RMS velocity of one of these molecules? (e) How much heat is required to raise the temperature of the gas to 35⁰ C if the volume is not changed as the heat is added? (f) How much heat is required to raise the temperature of the gas to 35º C if the volume is allowed to change in such a way that the pressure is not changed? (g) What is the change in internal energy of the gas during each of the two previous processes?

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

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Concept explainers

Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.

Question

**Nitrogen Gas Molecules Experiment**

A collection of nitrogen gas molecules is at \( P = 100,000 \, \text{Pa}, \, T = 25^\circ \, \text{C} \), and is held in a box of Volume \( V = 2 \, \text{m}^3 \). Answer all the following:

(a) **How many molecules are in the box?**

(b) **What is the average Translational Kinetic Energy of one of these molecules?**

(c) **What is the RMS (Root Mean Square) velocity of one of these molecules?**

(d) **What is the internal energy of the system?**

(e) **How much heat is required to raise the temperature of the gas to \( 35^\circ \, \text{C} \) if the volume is not changed as the heat is added?**

(f) **How much heat is required to raise the temperature of the gas to \( 35^\circ \, \text{C} \) if the volume is allowed to change in such a way that the pressure is not changed?**

(g) **What is the change in internal energy of the gas during each of the two previous processes?**

This exercise involves calculations using the ideal gas law, kinetic theory of gases, and thermodynamics, focusing on changes in energy and molecular behavior under different conditions.

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