**Problem Statement:**Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms (root mean square) speed of the atoms are expressed in terms of \( m \) and \( v_{\text{rms}} \) respectively (see the table). Suppose that \( m = 2.68 \times 10^{-26} \) kg, and \( v_{\text{rms}} = 1000 \) m/s. Find the temperature of the gas in each tank.**Table:**| | A | B | C | D ||---------|:---------:|:----------:|:-------:|:----------:|| **Mass** | \( m \) | \( m \) | \( 2m \) | \( 2m \) || **Rms speed** | \( v_{\text{rms}} \) | \( 2v_{\text{rms}} \) | \( v_{\text{rms}} \) | \( 2v_{\text{rms}} \) |Given:- \( m = 2.68 \times 10^{-26} \) kg- \( v_{\text{rms}} = 1000 \) m/s**Solution:**To find the temperature of the gas in each tank, we use the relationship for the rms speed in terms of temperature \( T \) for a monatomic ideal gas:\[ v_{\text{rms}} = \sqrt{\frac{3k_BT}{m}} \]Where:- \( v_{\text{rms}} \) is the rms speed of the gas particles,- \( k_B \) is the Boltzmann constant (\( 1.38 \times 10^{-23} \) J/K),- \( T \) is the absolute temperature,- \( m \) is the mass of one atom.By rearranging the formula, we solve for \( T \):\[ T = \frac{m v_{\text{rms}}^2}{3k_B} \]Calculating for each tank:1. **Tank A:** - Mass = \( m = 2.68 \times 10^{-26} \) kg - Rms speed = \( v_{\text

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Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms speed of the atoms are expressed in terms of m and Vrms respectively (see the table). Suppose that m = 2.68 x 10-26 kg, and Vrms = 1000 m/s. Find the temperature of the gas in each tank. Mass Rms speed A m Urms B m 20rms C 2m Urms D 2m 20rms

Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms speed of the atoms are expressed in terms of m and Vrms respectively (see the table). Suppose that m = 2.68 x 10-26 kg, and Vrms = 1000 m/s. Find the temperature of the gas in each tank. Mass Rms speed A m Urms B m 20rms C 2m Urms D 2m 20rms

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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