Air is filled in a motor tube at 27^∘ C and at a Pressure of 8 atmosphere. The tube suddenly bur

step 1 Hello students, in the question it is given that air is filled in a motor tube at 27 degrees cen

Air is filled in a motor tube at 27^∘ C and at a Pressure of...

Air is filled in a motor tube at $27^{\circ} \mathrm{C}$ and at a Pressure of 8 atmosphere. The tube suddenly bursts. Then what is the temperature of air. given $\gamma$ of air $=1.5$
(A) $150 \mathrm{~K}$
(B) $150^{\circ} \mathrm{C}$
(C) $75 \mathrm{~K}$
(D) $27.5^{\circ} \mathrm{C}$

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is transferred into or out of the system. In such a process, all changes in the internal energy of the system are due solely to work done on or by the system. This concept is central in thermodynamics when analyzing rapid processes where there isn’t enough time for heat exchange, a scenario often assumed in sudden expansions.

Reversible vs Irreversible Processes

Reversible processes occur infinitely slowly so that the system remains in thermodynamic equilibrium at all times, allowing the use of equilibrium relations. In contrast, irreversible processes, such as a sudden burst or free expansion, occur rapidly and the system does not remain in equilibrium. This distinction is crucial because applying formulas derived for reversible processes (like the adiabatic relation) to an irreversible process can lead to incorrect conclusions about state variables such as temperature.

Joule Expansion

Joule expansion describes a process in which a gas expands into a vacuum or into a region with negligible opposing pressure, doing no work in the process. For an ideal gas in a free expansion, the internal energy remains constant, meaning there is no change in temperature even though the gas expands. This concept is key when evaluating sudden expansions where the typical work or heat exchange mechanisms do not apply.

Specific Heat Ratio (?)

The specific heat ratio, denoted as ?, is the ratio of the specific heat at constant pressure to that at constant volume. It is a crucial parameter in the analysis of adiabatic processes because it appears in the adiabatic relations that connect pressure, volume, and temperature for an ideal gas. The value of ? influences how much the temperature of a gas changes during a reversible adiabatic transformation. However, its direct application may be misleading when the process is irreversible.

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