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2 moles of a diatomic gas are enclosed in a vessel. When a certain amount of heat is supplied,50% of gas molecules get dissociated, but there is not rise in temperature. What is the heat supplied, if temperature is T. a)RT b)RT/2 3)11/2RT 4)5RT

2 moles of a diatomic gas  are enclosed in a vessel. When a certain amount of heat is supplied,50% of gas molecules get dissociated, but there is not rise in temperature. What is the heat supplied, if temperature is T.
a)RT     b)RT/2      3)11/2RT        4)5RT

Grade:11

3 Answers

arun
123 Points
8 years ago
as there is no rise in temprature so \Delta U=0
initial number of moles = 2 
final number of moles = 3
now from first law of thermodynamics
\Delta Q= \Delta U+P\Delta V
\Delta Q= \Delta U+\Delta n\times RT
\Delta Q= RT                                       \left [ \because \Delta n=1 \right ]
so heat given is RT
Ashish
13 Points
5 years ago
Correct answer should be RT/2.
Initially total internal energy Ui=no. of moles × 5R/2 (since it is a diatomic gas)
Finally after supplying heat there are 1 mole of diatomic gas and 2 moles of monoatomic gas.
So final internal energy is Uf=5R/2+2×3R/2=11R/2-10R/2 = R/2.
 
So heat supplied is 11R/2-10
 
Triple Fire
13 Points
5 years ago
Given; 
Initial moles =2 
Final moles = 3 , (1mole of diatomic and 2 moles of 50 % dissapiated monoatomic molecules.)
∆T =0 and P∆V=nR∆T
U=1/2nfRT ; f= degree of freedom.
∆Q=∆U-P∆V=>∆Q=∆U
 
∆U= 1/2*2*5RT -1/2*3*3RT=RT/2 correct answer.
 
F for diatomic is 5 and for monoatomic is 3 
Hope it helps you clear your doubt

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