Adiabatic Process: Cv (Molar Heat)

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In summary, in this conversation, the topic is about a cylinder divided into two parts by a piston, with an ideal gas on the left and an unstretched spring on the right. After releasing the piston, the gas' volume doubles and its temperature is 10/11 of the initial temperature. The goal is to find the molar heat, Cv. The conversation discusses using the equation T V γ-1=constant, and the concept of adiabatic expansion, but there is confusion about the correct method to use. The conversation ends with the realization that the situation is not quasi-static, so the conservation of energy equation is the only applicable one.
  • #1
C_Ovidiu
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Say we have a cilinder, thermally isolated from the environment, divided in two parts by a piston. In the left part we have an ideal gas, in the right part an unstretched spring. After we set free the piston, in the final phase, we fin that the gas' volume has doubled, while it's temperature is 10/11 the initial temperature. Find Cv (molar heat).

If we consider [tex]L=-\Delta U[/tex] that we find a reasonable result. However, since the process is adibatic(that is why I used equation above) if we try to aply the formula [tex]T\cdot V^{\gamma-1}=ct[/tex] we find a totally different result. Why is that ?
 
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Since nobody else has responded, I'll take a stab at it.

Using T V γ-1=constant should give the right answer.

Is L supposed to be work done by the piston? How did you use that to calculate γ?

What did you get for γ using the two methods?
 
  • #3
The formula for adiabatic expansion only applies in quasi-static situations. In your situation, the spring provides no force initially, so it is definitely not quasi-static. Only the conservation of energy equation applies.
 

Related to Adiabatic Process: Cv (Molar Heat)

1. What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no heat exchange between the system and its surroundings. This means that the change in internal energy of the system is equal to the work done on or by the system.

2. What is Cv in relation to an adiabatic process?

Cv, also known as the molar heat capacity at constant volume, is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius while keeping the volume constant. In an adiabatic process, Cv is used to calculate the change in internal energy of the system.

3. How is Cv different from Cp?

Cp, also known as the molar heat capacity at constant pressure, is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius while keeping the pressure constant. Unlike Cv, Cp takes into account the work done by the system against external pressure. In an adiabatic process, Cp is used to calculate the change in enthalpy of the system.

4. What is the relationship between Cv and Cp?

The relationship between Cv and Cp is given by the equation Cp = Cv + R, where R is the gas constant. This means that Cp is always greater than Cv, since it takes into account the work done by the system. In an adiabatic process, the difference between Cp and Cv becomes significant and is used to determine the change in enthalpy of the system.

5. How is adiabatic process used in real-life applications?

Adiabatic processes are commonly used in the design and operation of heat engines, such as car engines and gas turbines. They are also used in the field of meteorology to study atmospheric processes and the behavior of air masses. Additionally, adiabatic processes are important in the study of thermodynamics and are used to understand the behavior of various substances under changing conditions.

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