When gases are mixed, the internal energy will remain conserved. When external energy provides heat energy there may be temperature variation leading to internal energy change and / or volume variation spending / giving work / energy. The change is internal energy is independent of the path followed, while work and heat energy depends on the path followed. Internal energy depends on the number of degrees of freedom which in turn affects the ratio of specific heat capacities.
(i)Two perfect gases of n 1 and n 2 moles at absolute temperatures T 1 and T 2 are mixed. The temperature of the mixture will be –
Text Solution
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Ans.
(i)
Sol. Net energy should be conserved.
n 1 E 1 + n 2 E 2 = (n 1 + n 2 )E
n 1 
kT 1 + n 2 
kT 2 = (n 1 + n 2 ) 
kT
∴ T = 
(ii)
Sol. We know that for f degree of freedom,
C V = 
R and C p = 
R + R
= 
R
γ = 
= 
= 1 + 
∴ f = 
(iii)
Sol. dU is path independent and is only a state function. In all process with equal dT, dU is same.
So choice is correct.
Ans.
(i)
Sol. Net energy should be conserved.
n 1 E 1 + n 2 E 2 = (n 1 + n 2 )E
n 1 
kT 1 + n 2 
kT 2 = (n 1 + n 2 ) 
kT
∴ T = 
(ii)
Sol. We know that for f degree of freedom,
C V = 
R and C p = 
R + R
= 
R
γ = 
= 
= 1 + 
∴ f = 
(iii)
Sol. dU is path independent and is only a state function. In all process with equal dT, dU is same.
So choice is correct.
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