To estimate the change in internal energy of the gas we need to understand the work done in growth and the amount of heat transfer.
The internal energy of the gas is 4189.6 J.
To estimate the work done we require the volume change. So we begin with the analysis of volume change. Consider the gas to be ideal.
Change in volume, ∆V= n R( [tex]T_{2} - T_{1}[/tex])/ P
∆V = 7.33 mol [tex]*[/tex] 0.082 L atm [tex]K^{-1}[/tex][tex]mol^{-1 }[/tex] [tex]*[/tex] 27.5 K/ 1 atm
∆V = 16.53 L
Work done in expansion, W = - P [tex]*[/tex] ∆V
= - 1 atm [tex]*[/tex] 16.53 L
= - 16.53 L atm
= -16.53 L atm [tex]*[/tex] (8.314 J/0.082 L atm)
= - 1676 J( 0.082 L atm = 8.314 J)
Heat transfer, [tex]Q = n* Cp*(T_{2} - T_{1} )[/tex]
= 7.33 mol [tex]*[/tex] 3.5 [tex]*[/tex] 8.314 J [tex]K^{-1[/tex] [tex]mol^{-1[/tex] [tex]*[/tex] 27.5 K
= 5865.6J
( Note: Cp = 3.5 [tex]*[/tex] R, the gas exists diatomic)
From the first law of thermodynamics,
∆E = Q + W
= 5865.6J - 1676 J
= 4189.6 J
Therefore, the internal energy of the gas is 4189.6 J.
To learn more first law of thermodynamics about refer to:
https://brainly.com/question/19863474
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