A monoatomic gas for it γ=(573) is suddenly Compressed to (1 / 8) of its original volume adiabat

step 1 Hello friends in the equation it is given that a monoatomic gas 4 8 gamma is given 5 by 3 is sud

A monoatomic gas for it γ=(573) is suddenly Compressed to (1...

A monoatomic gas for it $\gamma=(573)$ is suddenly Compressed to $(1 / 8)$ of its original volume adiabatically then the final Pressure of gas is ........... times its initial Pressure.
(A) 8
(B) 32
(C) $(24 / 5)$
(D) $(40 / 3)$

Key Concepts

Monoatomic Gas

A monoatomic gas consists of single atoms with minimal internal structure, which simplifies its thermodynamic behavior. The specific heat capacities for monoatomic gases lead to a specific heat ratio of about 5/3. This characteristic is crucial in applying the adiabatic equation correctly in thermodynamic problems involving gas compression or expansion.

Specific Heat Ratio (?)

The specific heat ratio, denoted by ?, is the ratio of the heat capacity at constant pressure (Cp) to that at constant volume (Cv). It reflects the degrees of freedom of the gas molecules and is critical in describing the behavior of gases during adiabatic processes. For a monoatomic gas, this value is typically 5/3, influencing how pressure and volume relate during compression or expansion.

Adiabatic Equation

The adiabatic equation, expressed as P · V^? = constant, relates the pressure and volume of a gas during an adiabatic process. It shows that when the volume of a system changes, the pressure adjusts in a power-law manner determined by the specific heat ratio (?). This relationship is essential for solving problems involving adiabatic compression or expansion.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. During such a process, any change in the internal energy of the system is solely due to work done on or by the system. This concept is fundamental in thermodynamics, particularly in deriving relationships between state variables under insulating conditions.

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