A piston-cylinder system contains 0.10 mole of ideal gas at 300 K. (a) If the gas expands isoth

step 1 belongs to the laws of thermodynamics in which we have a piston cylinder system containing numbe

A piston-cylinder system contains 0.10 mole of ideal gas at...

A piston-cylinder system contains 0.10 mole of ideal gas at $300 \mathrm{~K}$. (a) If the gas expands isothermally, does heat flow into the gas or out? (b) How much heat is required to expand the gas volume by a factor of $3 ?$

Key Concepts

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the process. For an ideal gas undergoing an isothermal transformation, this means that any heat added to the system must exactly compensate for the work done by the system, so that the internal energy (which for an ideal gas depends solely on temperature) stays unchanged.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a fundamental relationship among pressure, volume, temperature, and the amount of gas. This law is crucial when analyzing processes such as isothermal expansions since it links the macroscopic properties of a gas and allows us to calculate how pressure and volume change when the temperature is held constant.

Work Done in an Isothermal Process

In an isothermal process for an ideal gas, the work done by the system during expansion can be calculated by integrating the pressure with respect to volume. Because pressure is inversely proportional to volume in an isothermal process, the work expression involves a natural logarithm, capturing the cumulative effect of small changes in volume.

Heat Transfer and Energy Conservation

According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat transferred to the system minus the work done by the system. For an ideal gas in an isothermal process, the internal energy does not change, implying that the net heat flow must equal the work performed, so heat is absorbed by the gas if it does work on its surroundings.

Transcript

Please give Ace some feedback