What is the Ideal Gas Law for a Two-Bulb System with Varying Temperatures?

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SUMMARY

The discussion focuses on deriving the pressure equation for a two-bulb gas system with varying temperatures using the Ideal Gas Law. The final pressure, P, is expressed as P = (2P0(T1/T0)/(1+(T1/T2)), where P0 is the initial pressure, T0 is the initial temperature, T1 is the temperature of the first bulb, and T2 is the temperature of the second bulb. The analysis incorporates three equations based on the Ideal Gas Law, ensuring that the total number of gas particles remains constant throughout the process.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of thermodynamics, specifically temperature and pressure relationships
  • Familiarity with the concept of moles and particle conservation
  • Basic algebra for manipulating equations
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  • Study the Ideal Gas Law applications in multi-bulb systems
  • Explore thermodynamic principles related to gas behavior under varying temperatures
  • Investigate the concept of particle conservation in closed systems
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Students and professionals in physics, chemistry, and engineering who are interested in thermodynamics and gas laws, particularly those working with systems involving multiple gas containers and temperature variations.

Jean2005
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1. Two equal glass bulbs are connected by a narrow tube and the whole is initially filled with a gas at a temperature of T0 and pressure of P0. Then, one of the bulbs is immersed in a bath at a temperature, T1 and the other in a bath at a different temperature, T2. Show that in this problem, the overall pressure in the system changes to a value, P, give by this:

P= (2P0(T1/T0)/(1+(T1/T2)).

-need to use three equations using the ideal gas law, where one is for the combined system at the initial temperature and then an equation for each system after being immersed in the bath
-total number of particles is constant
 
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Please try to solve the problem by combining these three equations.

Also, have in mind that the sum of the moles of the two glass bulbs is constant as you said previously.
 

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