A 25-ft^3 insulated, rigid tank contains air at 110 16 f /...

A $25-\mathrm{ft}^{3}$ insulated, rigid tank contains air at 110 $16 f /$ in. $^{2}, 75$ F. A valve on the tank is opened, and the pressure inside quickly drops to 15 lbf/in." at which point the valve is closed. Assuming that the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass withdrawn during the process.

Key Concepts

Reversible Adiabatic Process

An adiabatic process is one in which no heat is transferred in or out of the system. When the process is reversible, it is also isentropic, meaning that the entropy remains constant. This concept is key when evaluating state changes in an insulated system, as it governs the relationship between pressure and temperature during expansion or compression.

Rigid Tank (Constant Volume) Behavior

In a rigid tank, the volume is fixed, which means that during any process the internal energy change must come solely from work interactions and changes in mass or temperature. This constraint simplifies the analysis since the absence of volume change (or expansion work) requires that pressure and temperature adjustments reflect energy conservation and thermodynamic process characteristics.

Ideal Gas Law

This fundamental relation connects pressure, volume, and temperature of a gas with its mass (or number of moles) through a constant specific to the gas. It is used to determine any one of these state variables when the others are known and is crucial for analyzing processes involving gases in fixed or variable volumes.

Mass Conservation in Systems with Mass Withdrawal

When a system allows mass to leave or enter, conservation of mass principles are used to account for the amount withdrawn or added. It involves comparing the initial mass with the final mass remaining in the system and is critical for determining the quantity of substance removed during processes like the reversible adiabatic expansion described.

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