Do [thermodynamics] A gas with an initial volume V1=0.3 m^3 is compressed from P1=100 kPa to P2

Name: Problem 1, Chapter 5: Engineering Mathematics Through Applications
Uploaded: 2025-03-14T04:31:14-08:00
Duration: 2 min 14 s
Channel: Mukesh Devi
Description: Do [thermodynamics] A gas with an initial volume V1=0.3 m^3 is compressed from P1=100 kPa to P2=350 kPa . From the formula P1(V1)^5 / 3=P2(V2)^5 / 3 evaluate the final volume V2. (Pascal, Pa=N / m^2, is the named SI unit of pressure.)

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

Question

Do [thermodynamics] A gas with an initial volume $V_{1}=0.3 \mathrm{~m}^{3}$ is compressed from $P_{1}=100 \mathrm{kPa}$ to $P_{2}=350 \mathrm{kPa} .$ From the formula $$ P_{1}\left(V_{1}\right)^{5 / 3}=P_{2}\left(V_{2}\right)^{5 / 3} $$ evaluate the final volume $V_{2}$. (Pascal, $\mathrm{Pa}=\mathrm{N} / \mathrm{m}^{2}$, is the named SI unit of pressure.)

   Do [thermodynamics] A gas with an initial volume $V_{1}=0.3 \mathrm{~m}^{3}$ is compressed from $P_{1}=100 \mathrm{kPa}$ to $P_{2}=350 \mathrm{kPa} .$
From the formula
$$
P_{1}\left(V_{1}\right)^{5 / 3}=P_{2}\left(V_{2}\right)^{5 / 3}
$$
evaluate the final volume $V_{2}$. (Pascal, $\mathrm{Pa}=\mathrm{N} / \mathrm{m}^{2}$, is the named SI unit of pressure.)

Engineering Mathematics Through Applications

Kuldeep Singh 2nd Edition

Chapter 5, Problem 1

Instant Answer

Solved by Expert Mukesh Devi

03/14/2025

Step 1

We have $P_1 = 100\,\text{kPa}$, $V_1 = 0.3\,\text{m}^3$, and $P_2 = 350\,\text{kPa}$. Show more…

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Do [thermodynamics] A gas with an initial volume $V_{1}=0.3 \mathrm{~m}^{3}$ is compressed from $P_{1}=100 \mathrm{kPa}$ to $P_{2}=350 \mathrm{kPa} .$ From the formula $$ P_{1}\left(V_{1}\right)^{5 / 3}=P_{2}\left(V_{2}\right)^{5 / 3} $$ evaluate the final volume $V_{2}$. (Pascal, $\mathrm{Pa}=\mathrm{N} / \mathrm{m}^{2}$, is the named SI unit of pressure.)

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Key Concepts

Adiabatic Process

An adiabatic process is a thermodynamic transformation during which a system does not exchange heat with its surroundings. In such a process, any change in the system's internal energy is entirely due to work done on or by the system, and the relationship between pressure and volume is characterized by the constant P·V^(?).

Specific Heat Ratio

The specific heat ratio, often symbolized by ? (gamma), is the ratio of the heat capacities at constant pressure and constant volume. It is crucial in describing the behavior of gases during adiabatic processes. For instance, a gamma value of 5/3 is typical for monatomic ideal gases, and it determines how pressure and volume are interrelated when no heat is exchanged.

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