A monatomic ideal gas that is initially at a pressure of 1.50 ×10^5 Pa and has a volume of 0.080

step 1 Solving party given that P1 is equal to 1 .5 into 10 power 5 PA and V1 is given as this value. V

A monatomic ideal gas that is initially at a pressure of...

A monatomic ideal gas that is initially at a pressure of $1.50 \times 10^{5} \mathrm{Pa}$ and has a volume of 0.0800 $\mathrm{m}^{3}$ is compressed adiabatically to a volume of $0.0400 \mathrm{m}^{3} .$ (a) What is the final pressure? (b) How much work is done by the gas?(c) What is the ratio of the final temperature of the gas to its initial temperature? Is the gas heated or cooled by this compression?

Key Concepts

Ideal Gas

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. Its behavior is defined by the ideal gas law, PV = nRT, which relates pressure, volume, temperature, and the amount of gas. This concept underpins the analysis of many thermodynamic processes, including adiabatic changes, by providing the fundamental relationships between state variables.

Adiabatic Process

An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings. All the change in the internal energy of the gas comes from work done during the process. In such processes, energy conservation simplifies to a relation between work and changes in internal energy, and the process is often characterized by changes in temperature.

Adiabatic Relations

In an adiabatic process for an ideal gas, the thermodynamic variables are related by equations such as PV^? = constant and TV^(?-1) = constant, where ? is the heat capacity ratio (C_p/C_v). These relations allow one to predict how pressure, volume, and temperature change relative to one another when no heat is exchanged with the surroundings.

Work in Thermodynamic Processes

Work in a thermodynamic process is the energy transferred by or to the system due to a force acting over a distance, typically represented in processes involving changes in volume. In the context of an adiabatic process, work done by or on the gas can be calculated using specific formulas derived from the first law of thermodynamics, linking work to changes in pressure and volume.

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