Kinetic Theory Of Gases Question 76
Two thermally insulated vessels 1 and 2 are filled with air at temperatures $ T_1 $ and $ 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] $ \frac{P(V _{1}+V _{2})}{T}=\frac{P _{1}V _{1}}{T _{1}}+\frac{P _{2}V _{2}}{T _{2}} $ ?.(i) Also $ P(V _{1}+V _{2}),=P _{1}V _{1}+P _{2}V _{2} $ ?(ii) After solving above equations, we get $ T=[ \frac{( P _{1}V _{1}+P _{2}V _{2} )T _{1}T _{2}}{P _{1}V {1}T{1}+P _{2}V _{2}T _{2}} ] $
BETA
