Adiabatic Equation Derivation Troubleshooting

In summary, an adiabatic tube HW problem involves calculating the temperature change of a gas as it flows through a tube with insulated walls. To solve this type of problem, the adiabatic equation can be used, and the initial and final conditions of the gas must be known. The main difference between adiabatic tube HW problems and isothermal processes is the assumption of heat transfer. These types of problems have various real-world applications, but some challenges include accuracy of assumptions and the complexity of the calculations involved.
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MotoPayton
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I have been struggling to find my mistake for over 2 hours now and I still haven't exactly matched my answers with the books solution. I feel that my method should give the same answer the solution manual obtained however they are slightly off.

I understand the book method completely.

Can someone tell me why my method doesn't work or find a way to make it work. I won't be able to sleep until I know.

Thanks

Book Question:

Capture-2.jpg


Book Solution:

solution.jpg


My solution:

DSCN8328.jpg


Derivation of adiabatic equation to avoid confusion:

DSCN8329.jpg

 
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FAQ: Adiabatic Equation Derivation Troubleshooting

What is an adiabatic tube HW problem?

An adiabatic tube HW problem is a scientific question that involves calculating the temperature change of a gas as it flows through a tube with insulated walls. This type of problem assumes that there is no heat transfer between the gas and its surroundings, making it an isothermal process.

How do you solve an adiabatic tube HW problem?

To solve an adiabatic tube HW problem, you will need to use the adiabatic equation: P1V1^γ = P2V2^γ, where P is pressure, V is volume, and γ is the ratio of specific heats. You will also need to know the initial and final conditions of the gas, such as pressure and volume. Plug these values into the equation and solve for the unknown variable.

What is the difference between an adiabatic tube HW problem and an isothermal process?

The main difference between an adiabatic tube HW problem and an isothermal process is the assumption of heat transfer between the gas and its surroundings. In an adiabatic process, there is no heat transfer, while in an isothermal process, the temperature of the gas remains constant due to heat transfer.

What are some real-world applications of adiabatic tube HW problems?

Adiabatic tube HW problems have various real-world applications, such as in the design of heat exchangers, refrigeration systems, and gas turbines. They are also used in the analysis of atmospheric temperature changes and in the study of fluid dynamics.

What are some challenges when solving adiabatic tube HW problems?

One of the main challenges when solving adiabatic tube HW problems is the accuracy of the assumptions made. In a real-world scenario, there may be some heat transfer between the gas and its surroundings, which can affect the results. Another challenge is the complexity of the calculations involved, as they often require multiple steps and equations to solve.

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