The pressure inside a tyre is 4 atm at 27^∘ C. If the tyre bursts suddenly, new temperature wil

step 1 In this question we have given that the pressure inside a tire is 4 atmospheric at 27 degrees Ce

The pressure inside a tyre is 4 atm at 27^∘ C. If the tyre...

The pressure inside a tyre is $4 \mathrm{~atm}$ at $27^{\circ} \mathrm{C}$. If the tyre bursts suddenly, new temperature will be $(\gamma=7 / 5)$
(a) $300(4)^{7 / 2}$
(b) $300(4)^{2 / 7}$
(c) $300(2)^{7 / 2}$
(d) $300(4)^{-2 / 7}$

Key Concepts

Pressure-Temperature Relationship in Adiabatic Processes

In a reversible adiabatic process, the relation between temperature and pressure is given by T P^{(1-?)/?} = constant. This equation allows one to determine the change in temperature of a gas when its pressure changes without heat transfer. It is key to predicting how the temperature will adjust following an adiabatic expansion or compression.

Irreversible Expansion

An irreversible expansion occurs when a gas expands rapidly, such as during the sudden bursting of a container. Although no heat is exchanged with the surroundings, the process is not quasi-static and does not follow the reversible adiabatic paths exactly. Nonetheless, reversible adiabatic formulas are often used as approximations to estimate the final state of the gas in such rapid, adiabatic processes.

Adiabatic Process

An adiabatic process is one in which a system does not exchange heat with its surroundings. In thermodynamics, the change in internal energy during such a process is solely due to the work done by or on the system. For gases, adiabatic changes lead to specific relationships between pressure, volume, and temperature, often expressed as PV^? = constant and T P^{(1-?)/?} = constant in reversible cases.

Specific Heat Ratio (?)

The specific heat ratio, denoted by ?, is the ratio of the specific heat at constant pressure (C_p) to the specific heat at constant volume (C_v). It is a critical parameter in understanding the behavior of gases during adiabatic processes, affecting how pressure and temperature change relative to each other when the gas undergoes expansion or compression.

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