Unsteady state process for first law of thermodynamics with changing boundries [closed]








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Firstly , this is not an homework question .I tried to solve this question to understand the concept.


[![enter image description here](https://i.stack.imgur.com/cncJm.jpg)](https://i.stack.imgur.com/cncJm.jpg)


I made the following attempt to solve this question.However I couldn't solve after exit valve is opened.Can you give me a hint or say my mistakes? 
From which boundry should I start to solve easily ?


[![enter image description here](https://i.stack.imgur.com/3kVN2.jpg)](https://i.stack.imgur.com/3kVN2.jpg)




Take as the system the air in the tank. Applying the open-system version of the first law of thermodynamics to this process, you have:


$$\Delta U=n\_fu\_f-n\_iu\_i=-p\_f(V\_f-V\_i)+(n\_f-n\_i)h\_s$$where $n\_i$ is the initial number of moles of air in the tank, $n\_f$ is the final number of moles of air in the tank, $u\_f$ is the final internal energy per mole of air in the tank, $u\_i$ is the initial internal energy per mole of air in the tank, $p\_f$ is the air pressure from the supply line, $V\_f$ is the final volume of air in the tank, $V\_i$ is the initial volume of air in the tank, and $h\_s=u\_i+RT\_i$ is the molar enthalpy of the air in the supply line.


The equation I wrote leads to a final answer which matches the correct answer given in the book.


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