Conceptual thermodynamics question regarding specific heat ratio

In summary, the conversation discusses finding a solution for an insulated rigid tank with air entering as an open system. The specific heat ratio is equal to the temperature ratio due to the open system version of the first law of thermodynamics. The equation used to solve the problem is Cv(Tfinal-Tin)=RTin, and the relation Cp=Cv+R is used to find the solution. The conversation ends with a thank you for the help.
  • #1
Andrew1234
18
1
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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  • #2
The tank is an open system where air enters. Are you familiar with the open-system version of the first law of thermodynamics?
 
  • #3
Yes I am familiar with the open system energy balance
 
  • #4
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?
 
  • #5
Thank you for your response.
Carnotcycle.png
 
  • #6
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?
 
  • #7
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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Likes Chestermiller

Related to Conceptual thermodynamics question regarding specific heat ratio

1. What is specific heat ratio?

The specific heat ratio, also known as the heat capacity ratio or adiabatic index, is a thermodynamic property that describes the ratio of the specific heats at constant pressure and constant volume for a given substance. It is denoted by the symbol γ.

2. How is specific heat ratio related to the state of a substance?

The specific heat ratio is a measure of the degree of freedom of a substance's molecules. It is related to the state of a substance because it determines the amount of energy required to change its temperature.

3. What is the significance of specific heat ratio in thermodynamics?

The specific heat ratio is an important parameter in thermodynamics as it helps in the calculation of various thermodynamic properties such as enthalpy, entropy, and internal energy. It also plays a crucial role in the analysis of thermodynamic processes.

4. How is specific heat ratio affected by temperature and pressure?

The specific heat ratio is affected by temperature and pressure. At higher temperatures, the specific heat ratio tends to decrease, while at higher pressures, it tends to increase. This is because the behavior of molecules changes with temperature and pressure, which affects their degree of freedom.

5. How can specific heat ratio be experimentally determined?

Specific heat ratio can be experimentally determined by measuring the speed of sound in a gas at different temperatures and pressures. The speed of sound is related to the specific heat ratio, allowing for its calculation. It can also be determined by using calorimetry techniques.

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