Final temperature in reversible expansion

In summary, the conversation discussed the expansion of one mole of an ideal monatomic gas in three reversible steps. The final volume was Cvi and the initial volume was Vi, with aVi and bVi representing the intermediate volumes. The equations used included TV^γ-1=C, Q=nrtln(V1V2), and ds= dq/dt. The answers calculated for a) final temperature, b) total heat transferred to gas, and c) total entropy change were 1000(a/b)^2/3, 1000Rlna + 1000R(a/b)^2/3ln(c/b), and Rln(ac/b) respectively. These answers were verified to be correct.
  • #1
twinklestar28
21
0

Homework Statement



One mole of an ideal monatomic gas initially at volume Vi and temperature 1000k expands to a final volume Cvi in three reversible steps: 1) isothermal expansion from Vi to aVi, 2) adiabatic expansion from aVi to bVi and 3) isothermal expansion from bVi to Cvi

In terms of a,b,c calculate
a) final temperature
b) total heat transferred to gas
c) total entropy change


Homework Equations



TV^γ-1=C
Q=nrtln(V1V2)
ds= dq/dt


The Attempt at a Solution



a) final temperature = 1000(a/b)^2/3

b) heat transferred = 1000Rlna + 1000R(a/b)^2/3ln(c/b)

c) entropy change = Rln(ac/b)

Could someone check these for me please?
 
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  • #2
Your answers look correct to me.
 
  • #3
ok thanks alot
 

What is the concept of final temperature in reversible expansion?

The concept of final temperature in reversible expansion refers to the temperature at which a system reaches equilibrium after undergoing a reversible expansion process. It is a thermodynamic property that takes into account the initial temperature, pressure, and volume of the system, as well as the work done on or by the system during the expansion.

How is final temperature calculated in reversible expansion?

The final temperature in reversible expansion can be calculated using the ideal gas law, which states that the product of pressure and volume is directly proportional to the temperature. By rearranging the equation to solve for temperature, the final temperature can be determined by plugging in the initial conditions and the work done on or by the system.

What is the difference between final temperature and equilibrium temperature?

The final temperature in reversible expansion is the temperature at which a system reaches equilibrium after undergoing a reversible expansion process. On the other hand, equilibrium temperature is the temperature at which two or more substances or systems reach thermal equilibrium after being in contact with each other. While final temperature is specific to a single system, equilibrium temperature is a property of the entire system.

Why is final temperature important in reversible expansion?

Final temperature is important in reversible expansion because it helps determine the efficiency of the expansion process. In a reversible expansion, the final temperature is the same as the initial temperature, indicating that the process is highly efficient and there is no loss of energy. On the other hand, in an irreversible expansion, the final temperature may be different from the initial temperature, indicating a loss of energy.

What factors can affect the final temperature in reversible expansion?

The final temperature in reversible expansion can be affected by the initial conditions of the system (such as temperature, pressure, and volume), the amount of work done on or by the system, and the properties of the gas being expanded. Additionally, if the expansion is not carried out in a perfectly reversible manner, the final temperature may also be influenced by factors such as friction and heat transfer.

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