Air from a line at 1800 lbfin. ^2, 60 F flows into a 20-ft^3 rigid tank that initially containe

step 1 So let's solve this question. So in this question, we have M1 equals to P1 v by RT1, that equals

Air from a line at 1800 lbfin. ^2, 60 F flows into a...

Air from a line at 1800 lbfin. ${ }^{2}, 60$ F flows into a $20-\mathrm{ft}^{3}$ rigid tank that initially contained air at ambient conditions, $14.7 \mathrm{lbf} / \mathrm{in}^{2}, 60 \mathrm{~F}$. The process occurs rapidly and is essentially adiabatic. The valve is closed when the pressure inside reaches some value, $P_{2}$. The tank eventually cools to room temperature, at which time the pressure inside is $750 \mathrm{lbf} / \mathrm{in}^{2}$. What is the pressure $P_{2} ?$ What is the net entropy change for the overall process?

Key Concepts

Energy Conservation (First Law of Thermodynamics)

The first law of thermodynamics, or the principle of energy conservation, states that the energy of a closed system remains constant unless energy is added or removed. In processes where mass flows into a system, the energy carried by the arriving mass alters the internal energy and observable properties like pressure and temperature.

Mass Addition and Mixing Processes

When mass is added to a system, as in the case of air entering a tank, the system’s properties such as pressure and temperature change. Analyzing such mixing or mass addition processes requires applying conservation laws to account for the additional mass and energy, ultimately affecting the state of the system.

Entropy Change and Irreversibility

Entropy is a measure of disorder and the number of microscopic configurations available to a system. The net entropy change in a process helps indicate the degree of irreversibility; irreversible processes, such as rapid mixing or adiabatic mass addition, typically result in an increase in the total entropy of the universe, reflecting the inherent inefficiencies in real systems.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. In thermodynamics, such processes are characterized by changes in internal energy that are solely due to work or mass flows rather than heat transfer, and they are especially important when dealing with rapid or insulated processes.

Constant-Volume Process

A constant-volume process describes a situation where the system's volume remains unchanged throughout the process, such as in a rigid tank. Because the volume is fixed, no work is performed due to expansion or compression, and any energy changes come solely from mass addition or internal energy variations.

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