Thermodynamics Problem - Adiabatic Reversible Process....

In summary, the conversation discusses the calculation of the pressure of a gas in its final state after undergoing a reversible adiabatic process. The gas has a specific heat capacity at constant pressure that is a function of temperature, with a specific ideal gas constant. The method for calculating the pressure is correct, but there may be an error in the value used for the linear relationship between temperature and cp.
  • #1
Allison Barry
3
0
Homework Statement
A specific type of ideal gas has a specific heat capacity at constant pressure (cp=cv+R) that is a function of temperature T, such that cp=0.5+876T, where cp has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 294 K and P1 = 1x105 Pa, undergoes a reversible adiabatic process such that its final temperature is T2 = 778 K. Calculate the pressure of the gas (in Pa) in this final state. Assume the following ideal gas constant: R = 287 J/kg/K. Recall that ds = cpdT/T – RdP/P.

Relevant equations
Reversible Adiabatic process:
Entropy is 0 because this is adiabatic and reversible.
Constituitive relation for entropy of such a process is:
S2 - S1 = ∫12dS = 0
dS = cp(dT/T) - R(dP/P) = 0
Attempt:
Integrating I got:
T1T2(0.5 + 876T).(dT/T) - 287∫P1P2(dP/P)
876(778 - 294) + (0.5) ln (778/294) = 287ln(P2 / 100,000Pa)
Getting 1488.810788 = lnP2

But e1488.810788 is undefinable? I am confused? Did I integrate this wrong?
 
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  • #2
That 876 looks very, very, very suspicious. Are you sure it's not 0.0876 or 0.00876 or, more likely, 0.000876? There's definitely something wrong here.

Your methodology and arithmetic are correct, however.

Chet
 
  • #3
Chestermiller said:
That 876 looks very, very, very suspicious. Are you sure it's not 0.0876 or 0.00876 or, more likely, 0.000876? There's definitely something wrong here.

Your methodology and arithmetic are correct, however.

Chet
876 is part of "a +bt", the linear relationship between temperature and Cp, it's 0.5 + 876T
 
  • #4
Allison Barry said:
876 is part of "a +bt", the linear relationship between temperature and Cp, it's 0.5 + 876T
What I'm saying is that there is something wrong with that value. It can't be correct.
 

1. What is an adiabatic reversible process?

An adiabatic reversible process is a thermodynamic process in which there is no transfer of heat between the system and its surroundings, and the process occurs without any irreversibilities or losses. This means that the system is perfectly insulated and the process is reversible, meaning it can be reversed without any energy losses.

2. How is an adiabatic reversible process different from an adiabatic irreversible process?

An adiabatic irreversible process is also a process in which there is no transfer of heat between the system and its surroundings. However, unlike an adiabatic reversible process, an adiabatic irreversible process involves some form of irreversibility or energy loss, such as friction or turbulence. This means that the process cannot be reversed without some energy losses.

3. What is the mathematical equation for an adiabatic reversible process?

The mathematical equation for an adiabatic reversible process is Q = 0, where Q represents the heat transfer between the system and its surroundings. This means that in an adiabatic reversible process, there is no heat transfer between the system and its surroundings.

4. What is the significance of an adiabatic reversible process in thermodynamics?

An adiabatic reversible process is significant in thermodynamics because it represents an idealized process that allows for the analysis of thermodynamic systems without any energy losses. It helps to understand the maximum potential work that can be obtained from a system and is used as a benchmark to compare with real-world processes.

5. Can all processes be considered adiabatic reversible processes?

No, not all processes can be considered adiabatic reversible processes. Real-world processes involve some form of energy loss or irreversibility, meaning they cannot be perfectly insulated or reversed without losses. Adiabatic reversible processes are idealized and used for theoretical analysis and comparison with real-world processes.

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