[W] [thermodynamics] A gas in a cylinder with an initial volume V1=0.25 m^3 and pressure P1=100

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

[W] [thermodynamics] A gas in a cylinder with an initial...

[W] [thermodynamics] A gas in a cylinder with an initial volume $V_{1}=0.25 \mathrm{~m}^{3}$ and pressure $P_{1}=100 \mathrm{kPa}$ is compressed to a final pressure $P_{2}=450 \mathrm{kPa}$. Given that $$ P_{1}\left(V_{1}\right)^{1.33}=P_{2}\left(V_{2}\right)^{1.33} $$ determine the final volume $V_{2}$.

[W] [thermodynamics] A gas in a cylinder with an initial volume $V_{1}=0.25 \mathrm{~m}^{3}$ and pressure $P_{1}=100 \mathrm{kPa}$ is compressed to a final pressure $P_{2}=450 \mathrm{kPa}$. Given that
$$
P_{1}\left(V_{1}\right)^{1.33}=P_{2}\left(V_{2}\right)^{1.33}
$$
determine the final volume $V_{2}$.

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Key Concepts

Exponentiation and Algebraic Manipulation

Many thermodynamics problems involve equations where variables are raised to a power, requiring the use of exponentiation and algebraic manipulation to solve for an unknown quantity. This skill is crucial when rearranging expressions such as P1·V1^n = P2·V2^n to isolate and compute the desired variable.

Gas Compression

Gas compression refers to the process of reducing the volume of a gas, which typically results in an increase in pressure. Understanding the relationship between pressure and volume during compression, especially under a defined process such as a polytropic transformation, is essential for predicting how the state of the gas changes.

Polytropic Process

A polytropic process is a thermodynamic process that can be described by the equation P·V^n = constant, where P is the pressure, V is the volume, and n is the polytropic exponent. This relationship generalizes various types of processes, including isothermal and adiabatic processes, depending on the value of n, and is useful for analyzing compression and expansion in gases.

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