Academic First Law Of Thermodynamics Problem

In summary, the conversation discusses a problem involving the application of the open-system version of the 1st law of thermodynamics. The solution should be formulated as a time-dependent differential equation and for constant temperature, it reduces to 0=-W+VdP/dt. There is a discussion about the disappearance of the term udn/dt in the equation and its cancellation from both sides of the equation. The conversation also touches on the derivative of un with respect to t and the terms h=u+Pv.
  • #1
Kolin101
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Homework Statement
An insulated tank of volume 12 m3 and with a valve was filled with perfect triatomic gas at pressure 10 bar. Initially the valve was closed. A paddle wheel was mounted inside the tank and was run by 20 kW engine. The paddle wheel was turn on and at the same time the exit valve was opened. The gas temperature was constant trough the whole process (due to very slow flow) and equal to 300 K.
Calculate the time needed to decrease the pressure in the tank to 5 bar.
Relevant Equations
dU=dQ-dW-dmh
Hi there. I have a problem solving above problem. How can I move on with my solution? It seems to me that I have proper approach but I'm just stuck with the energy equation ;/

Part of solution below:

Exam Questions Test 1 - Strona 1.jpg
 
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  • #2
This involves application of the open-system version of the 1st law of thermodynamics, and, for this particular problem, should be formulated as a time-dependent differential equation (rather than using finite differences): $$\frac{d(nu)}{dt}=-\dot{W}+h\frac{dn}{dt}=-\dot{W}+u\frac{dn}{dt}+RT\frac{dn}{dt}$$For constant temperature, this reduces to: $$0=-\dot{W}+V\frac{dP}{dt}$$
 
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  • #3
Thank You a lot, I've tried also this way but with no results. But to be sure, what for does the "n" stands for in your first equation?
 
  • #4
Kolin101 said:
Thank You a lot, I've tried also this way but with no results. But to be sure, what for does the "n" stands for in your first equation?
Number of moles in tank at time t.
 
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  • #5
ok I've figured out how would it look like in "my style solution" but I still have some questions. Why does the $$ u\frac{dn}{dt} $$
term disappears? when i rewrote it using mass instead of moles, the term
$$\frac{dm}{dt}CvT$$ seems to have a non zero value (there is a mass flowing out, that caries out internal energy at T=300K) and unfortunately Cv is not known either ;/

(new solution attached below the quote)
Chestermiller said:
This involves application of the open-system version of the 1st law of thermodynamics, and, for this particular problem, should be formulated as a time-dependent differential equation (rather than using finite differences): $$\frac{d(nu)}{dt}=-\dot{W}+h\frac{dn}{dt}=-\dot{W}+u\frac{dn}{dt}+RT\frac{dn}{dt}$$For constant temperature, this reduces to: $$0=-\dot{W}+V\frac{dP}{dt}$$

tank discharge.jpg
 
  • #6
Kolin101 said:
ok I've figured out how would it look like in "my style solution" but I still have some questions. Why does the $$ u\frac{dn}{dt} $$
term disappears?
It cancels from both sides of the equation. What is the derivative of un with respect to t? On the rhs, h=u+Pv.
 

1. What is the Academic First Law of Thermodynamics Problem?

The Academic First Law of Thermodynamics Problem is a fundamental law of physics that states that energy cannot be created or destroyed, only transferred or converted from one form to another. It is also known as the Law of Conservation of Energy.

2. How does the Academic First Law of Thermodynamics Problem apply to academic studies?

In academic studies, the First Law of Thermodynamics is used to understand and analyze energy transformations in various systems. It can be applied to fields such as chemistry, physics, and engineering to study the transfer and conversion of energy in different processes.

3. What are some real-life examples of the Academic First Law of Thermodynamics Problem?

Some real-life examples of the First Law of Thermodynamics include the conversion of chemical energy in food to mechanical energy in the body, the transfer of heat from a hot object to a cold one, and the conversion of electrical energy to light and heat in a light bulb.

4. How is the Academic First Law of Thermodynamics Problem related to the Second Law of Thermodynamics?

The First Law of Thermodynamics deals with the conservation of energy, while the Second Law of Thermodynamics deals with the direction of energy transfer and the increase of entropy in a closed system. Both laws work together to explain the behavior of energy in various systems.

5. What are some common misconceptions about the Academic First Law of Thermodynamics Problem?

One common misconception is that the First Law of Thermodynamics only applies to closed systems, when in fact it applies to all systems. Another misconception is that the First Law allows for perpetual motion machines, when in reality, it states that energy cannot be created or destroyed, but it can be converted from one form to another.

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