Calculating Final Temperature Using Ideal Gas Law | Homework Help

AI Thread Summary
To find the final temperature of the gas in the rigid tank after half of it escapes, the ideal gas law equation pV = mRT can be applied to both the initial and final states. The initial conditions include 5 kg of gas at 4 atm and 40°C, while the final pressure is given as 1.5 atm after the mass is reduced to 2.5 kg. The relationship between pressure, volume, and temperature must be maintained, allowing for the calculation of the final temperature using the known quantities. The problem emphasizes understanding how to apply the ideal gas law to different states of the system. The final temperature can be determined once the appropriate values are substituted into the equations.
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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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