A gas at a pressure of 2.10 ×10^5 Pa occupies 4.98 ×10^-3 m^3 in a chamber that can change its

step 1 So this problem asked to determine the final volume and the final temperature of the gas, given

A gas at a pressure of 2.10 ×10^5 Pa occupies 4.98 ×10^-3...

A gas at a pressure of $2.10 \times 10^{5}$ Pa occupies $4.98 \times 10^{-3} \mathrm{~m}^{3}$ in a chamber that can change its volume. The gas is at an initial temperature of $290 \mathrm{~K}$ when it is heated, so that it expands isobarically, thereupon doing $200 \mathrm{~J}$ of work. Determine the new volume and the final temperature of the gas. [Hint: Use Eq. (20.1) and the Ideal Gas Law applied before and after the expansion.]

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Key Concepts

Thermodynamic State Variables

Thermodynamic state variables such as pressure, volume, and temperature define the state of a system at equilibrium. Their interrelationships, governed by laws like the Ideal Gas Law, are essential for describing and predicting the behavior of gases during various thermodynamic processes.

Work in Thermodynamic Processes

In thermodynamics, work is the energy transfer resulting from a force acting through a distance. For processes involving gases, the work done during expansion or compression, particularly at constant pressure, is determined by the product of pressure and the change in volume and reflects the energy exchanged by the system with its surroundings.

Isobaric Process

An isobaric process is one in which the pressure of the gas remains constant. In such processes, changes in volume are directly related to changes in temperature, with the work done by or on the gas being calculated simply by multiplying the constant pressure by the change in volume.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates pressure, volume, temperature, and the number of moles of a gas. This fundamental equation in thermodynamics allows for the determination of one state variable if the others are known, making it critical for analyzing the behavior of gases under various conditions.

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