Conceptual thermodynamics question regarding specific heat ratio

AI Thread Summary
The discussion centers on understanding the relationship between the specific heat ratio and temperature ratio in an open system, specifically in the context of thermodynamics. Participants clarify the equations related to internal energy and enthalpy, emphasizing the importance of the first law of thermodynamics in analyzing an open system. The conversation highlights the derivation of the equation linking changes in internal energy to temperature changes, ultimately leading to the conclusion that the specific heat ratio can be expressed in terms of temperature ratios. The use of the relation Cp = Cv + R is acknowledged as a key step in solving the problem. Overall, the exchange aids in clarifying the conceptual underpinnings of thermodynamic principles in open systems.
Andrew1234
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Homework Statement
An insulated rigid tank is initially evacuated. A valve is opened, and atmospheric air at 95 kPa and 17 C enters the tank until the pressure in the tank reaches 95 kPa, at which point the valve is closed. Determine the final temperature of the air in the tank. Assume constant specific heats.
Relevant Equations
Cp=dh/dt
CV=du/dt
The solution can be found at https://study.com/academy/answer/an-insulated-rigi...

After using the two equations I can't see
why (h2-h1)/(u2) should equal (T2)/(T1).

Can someone explain why specific heat ratio is equal to temperature ratio?
 
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The tank is an open system where air enters. Are you familiar with the open-system version of the first law of thermodynamics?
 
Yes I am familiar with the open system energy balance
 
OK. So $$\Delta U=mu_{final}=mh_{in}=m(u_{in}+(Pv)_{in})$$where m is the final amount of mass that flows in. OK so far?
 
Thank you for your response.
Carnotcycle.png
 
Andrew1234 said:
Thank you for your response.
View attachment 259973
Well, from $$u_{final}=h_{in}=u_{in}+(Pv)_{in}$$ we have $$u_{final}-u_{in}=(Pv)_{in}$$or$$C_v(T_{final}-T_{in})=RT_{in}$$OK so far?
 
Yes, I understand the solution up to that point
I think I see how to solve the problem now, using the relation Cp = Cv+R
Thank you for your help
 
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