[D[thermodynamics] A volume, 0.1 m^3, of gas at a pressure of 200 kN / m^2 is compressed to a p

step 1 Now here in this problem we are given that a volume 0 .1 cubic meter at a pressure of 200 kilo N

[D[thermodynamics] A volume, 0.1 m^3, of gas at a pressure...

[D_[thermodynamics] A volume, $0.1 \mathrm{~m}^{3}$, of gas at a pressure of $200 \mathrm{kN} / \mathrm{m}^{2}$ is compressed to a pressure of $632 \mathrm{kN} / \mathrm{m}^{2}$. If the gas obeys the law
$$
P_{1} V_{1}{ }^{1.5}=P_{2} V_{2}{ }^{1.5}
$$
then find the new volume.

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Key Concepts

Polytropic Process

A polytropic process is a thermodynamic process that follows the relation PV^n = constant, where n is the polytropic exponent. This relation generalizes several types of processes; for example, when n equals the specific heat ratio ?, the process is adiabatic, and when n equals 1, it is isothermal. The polytropic equation is crucial for analyzing how changes in pressure and volume affect a gas during compression or expansion.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings; any change in the internal energy of the system comes solely from work done on or by the system. In the context of an ideal gas, the adiabatic process is expressed as PV^? = constant, where ? is the ratio of specific heats. This concept is important when understanding how gases behave under rapid compression or expansion without heat transfer.

Pressure-Volume Relationship

The pressure-volume relationship in thermodynamics describes how the pressure and volume of a gas are interconnected during a process. In processes governed by a law like PV^n = constant, knowing the initial state allows one to predict the final state if one of the variables, either pressure or volume, changes. This relationship is fundamental for solving problems involving the compression or expansion of gases.

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