Answer:
(a) ΔU=747J
(b) γ=1.3
Explanation:
For (a) change in internal energy
According to first law of thermodynamics the change in internal energy is given as
ΔU=Q-W
Substitute the given values
ΔU=970J-223J
ΔU=747J
For(b) γ for the gas.
We can calculate γ by ratio of heat capacities of the gas
γ=Cp/Cv
Where Cp is the molar heat capacity at constant pressure
Cv is the molar heat capacity at constant volume
To calculate γ we first need to find Cp and Cv
So
For Cp
As we know
Q=nCpΔT
Cp=(Q/nΔT)
[tex]C_{p}=\frac{970J}{1.75mol*(25^{o}C-10^{o}C )}\\C_{p}=37J/mol.K[/tex]
From relation of Cv and Cp we know that
Cp=Cv+R
Where R is gas constant equals to 8.314J/mol.K
So
[tex]C_{v}=C_{p}-R\\C_{v}=37-8.314\\C_{v}=28.687J/mol.K\\[/tex]
So
γ=Cp/Cv
γ=[(37J/mol.K) / (28.687J/mol.K)]
γ=1.3
