Answer:
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Step-by-step explanation:
To solve this problem, you need to use the first law of thermodynamics to analyze the combustion process that occurs in the constant-volume tank.
First, you need to determine the initial and final states of the system. The initial state is given as 1 lbmol of methane (CH₂) gas and 3 Ibmol of O₂ at 77°F and 1 atm. The final state is given as the same mixture of gases at 1800 R.
Next, you need to determine the heat transfer during the process. To do this, you can use the first law of thermodynamics in the form of the heat equation:
Q = ΔU + W
where Q is the heat transfer, ΔU is the change in internal energy, and W is the work done by the system.
Since the process occurs at constant volume, the work done by the system is zero. Therefore, the heat transfer can be calculated as:
Q = ΔU
You can then use the change in internal energy to determine the final pressure in the tank. The change in internal energy can be calculated using the internal energy of the reactants and products, which can be found from tables of thermochemical data or by using equations of state.
Once you have determined the heat transfer and the change in internal energy, you can use these values to calculate the final pressure in the tank using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
You can then use the values of the final temperature and the number of moles of gas in the tank to calculate the final pressure.
I hope this helps! Let me know if you have any questions.