Calculating Final Temperature Using Ideal Gas Law | Homework Help

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the final temperature of an ideal gas in a rigid tank after a portion of the gas escapes. Participants explore the application of the ideal gas law across two different states of the gas, focusing on the relationships between pressure, volume, mass, and temperature.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents the problem statement, indicating the initial conditions of the gas and the final pressure after half of the mass escapes.
  • Another participant suggests using the ideal gas law for both the initial and final states, proposing to set up equations for each state.
  • A third participant notes the lack of specific gas or fluid information, implying that this may affect the solution.
  • A later reply emphasizes that there is sufficient information to solve the problem, directing the original poster to consider the relationships between the known quantities.

Areas of Agreement / Disagreement

Participants generally agree that the ideal gas law can be applied to both states, but there is no consensus on the specific steps needed to arrive at the final temperature, as the original poster expresses uncertainty about how to proceed.

Contextual Notes

The discussion does not clarify the specific gas involved, which may influence the application of the ideal gas law. Additionally, the original poster's understanding of how to transition between the two states remains unresolved.

Who May Find This Useful

Students working on problems involving the ideal gas law, particularly in the context of thermodynamics and state changes in gases.

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Homework Statement


A rigid tank contains 5 kg of an ideal gas at 4 atm and T=40 deg C. Now, a valve is opened and half of the mass of the gas is allowed to escape. If the final pressure in the tank is 1.5 atm, the final temperature in the tank is?


Homework Equations



pV=mRT

The Attempt at a Solution



I know pV=mRT but I don't know how to use this equation for to different states i.e. beginning and end state.
 
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The equation holds for the two different states, so you have
\begin{align*}
p_i V_i &= m_i R T_i \\
p_f V_f &= m_f R T_f
\end{align*}
What are the quantities you know? What other relationship were you given that relates the quantities?
 
That is it. That is the whole problem statement. No specific gas or fluid was given.
 
I know. There's enough information to solve the problem. Those questions were meant for you to answer.
 

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