An amount Q of heat is given to a monoatomic ideal gas in a process in which the gas performs a work of 
on its surrounding. Then.
(i) Equation of the process –
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Ans.
(i)
Sol. Given, Δ W = 
As Δ Q = Δ U + Δ W
⇒ Δ U = 
∴ dU = dW
C V dT = PdV
= PdV
Substituting γ = 
and integrating
P 3 V = constant … (1)
Also, C = C V + 
= 3R
Again, PV = nRT … (2)
= constant
∴ T 3 ∝ V 2 (ii)
Sol. Given, Δ W = 
As Δ Q = Δ U + Δ W
⇒ Δ U = 
∴ dU = dW
C V dT = PdV
= PdV
Substituting γ = 
and integrating
P
3 V = constant … (1)
Also, C = C V + 
= 3R
Again, PV = nRT … (2)
= constant
∴ T 3 ∝ V 2
(iii)
Sol. Given, Δ W = 
As Δ Q = Δ U + Δ W
⇒ Δ U = 
∴ dU = dW
C V dT = PdV
= PdV
Substituting γ = 
and integrating
P 3 V = constant … (1)
Also, C = C V + 
= 3R
Again, PV = nRT … (2)
= constant
∴ T 3 ∝ V 2
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