Question

¿o [thermodynamics] A gas is expanded from an initial pressure $P_{1}$ and volume $V_{1}$ of $5 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{-4} \mathrm{~m}^{3}$respectively, to a final pressure $P_{2}=2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. Find the new volume $V_{2}$ given that $P_{1} V_{1}=P_{2} V_{2}$.

Name: Problem 3, Chapter 1: Engineering Mathematics Through Applications
Uploaded: 2025-03-14T04:31:14-08:00
Duration: 2 min 14 s
Channel: Mukesh Devi
Description: ¿o [thermodynamics] A gas is expanded from an initial pressure P1 and volume V1 of 5 ×10^6 N / m^2 and 2 ×10^-4 m^3respectively, to a final pressure P2=2 ×10^7 N / m^2. Find the new volume V2 given that P1 V1=P2 V2.

   ¿o [thermodynamics] A gas is expanded from an initial pressure $P_{1}$ and volume $V_{1}$ of $5 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{-4} \mathrm{~m}^{3}$respectively, to a final pressure $P_{2}=2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. Find the new volume $V_{2}$ given that $P_{1} V_{1}=P_{2} V_{2}$.

Engineering Mathematics Through Applications

Kuldeep Singh 2nd Edition

Chapter 1, Problem 3

Instant Answer

Solved by Expert Mukesh Devi

03/14/2025

Step 1

We are given the initial pressure $P_1$ and volume $V_1$ of a gas: $P_1 = 5 \times 10^6 \mathrm{~N/m^2}$ and $V_1 = 2 \times 10^{-4} \mathrm{~m^3}$. Show more…

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¿o [thermodynamics] A gas is expanded from an initial pressure $P_{1}$ and volume $V_{1}$ of $5 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{-4} \mathrm{~m}^{3}$respectively, to a final pressure $P_{2}=2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. Find the new volume $V_{2}$ given that $P_{1} V_{1}=P_{2} V_{2}$.

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Key Concepts

Boyle's Law

Boyle's Law is a principle in thermodynamics that states that the pressure of a given mass of an ideal gas is inversely proportional to its volume when the temperature is held constant. This means that as the volume of the gas increases, its pressure decreases proportionally, and vice versa. The relationship is mathematically expressed as P × V = constant, making it a fundamental concept in understanding the behavior of gases under compression or expansion in isothermal conditions.

Isothermal Process

An isothermal process is one in which the temperature remains constant throughout the change in state. In such processes, since the temperature does not change, the internal energy of an ideal gas remains constant, and according to Boyle's Law, the product of pressure and volume remains constant. This concept is key in analyzing expansions or compressions of gases where heat exchange with the environment maintains a constant temperature.

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