Kinetic Theory Of Gases Question 105
Question: Two thermally insulated vessels 1 and 2 are filled with air at temperatures $ (T _{1},T _{2}), $ volume $ (V _{1},V _{2}) $ and pressure $ (P _{1},P _{2}) $ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
Options:
A) $ T _{1}+T _{2} $
B) $ (T _{1}+T _{2})/2 $
C) $ \frac{T _{1}T _{2}(P _{1}V _{1}+P _{2}V _{2})}{P _{1}V _{1}T _{2}+P _{2}V _{2}T _{1}} $
D) $ \frac{T _{1}T _{2}(P _{1}V _{1}+P _{2}V _{2})}{P _{1}V _{1}T _{1}+P _{2}V _{2}T _{2}} $
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Answer:
Correct Answer: C
Solution:
[c] The number of moles of the system remains same, $ \frac{P _{1}V _{1}}{RT _{1}}+\frac{P _{2}V _{2}}{RT _{2}}=\frac{P(V _{1}+V _{2})}{RT} $
Therefore $ T=\frac{P(V _{1}+V _{2})T _{1}T _{2}}{(P _{1}V _{1}T _{2}+P _{2}V _{2}T _{1})} $ According to BoyleΒs law, $ P _{1}V _{1}+P _{2}V _{2}=P(V _{1}+V _{2}) $ \ $ T=\frac{(P _{1}V _{1}+P _{2}V _{2})T _{1}T _{2}}{(P _{1}V _{1}T _{2}+P _{2}V _{2}T _{1})} $
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