# Why Might Statement (b) Be Incorrect in Ideal Gas Processes?

• grangr
In summary, the correct statement when an ideal gas goes from an initial to a final state in a single process is (a), where no work is done on or by the gas when the volume remains constant. Statement (b) is incorrect because although there is no change in internal energy, there could still be heat transfer to balance the PV work done during a change in volume.
grangr

## Homework Statement

Which of the following statement(s) is (are) correct when an ideal gas goes from an initial to a final state in a single process?
a. No work is done on or by the gas when the volume remains constant.
b. No energy is transferred into or out of the gas as heat transfer when the temperature remains constant.
c. The internal energy of the gas does not change when the pressure remains constant.
d. All the statements above are correct.
e. Only statements (a) and (b) above are correct.​

## Homework Equations

• ΔH = ΔE + Δ(PV) = Q + W + Δ(PV), and for ideal gas, ΔH = nCvΔT + Δ(nRT) = nCvΔT + nRΔT = nCpΔT

## The Attempt at a Solution

The answer given is (a), while my attempt was (e). I do not understand why (b) is incorrect.

a. Given constant V, ΔV = 0, thus W = 0. (a) is correct.
b. Given constant T on ideal gas, ΔE (or ΔU, internal energy) = 0, thus there is no energy transferred as heat in or out of the system. But why is (b) incorrect then?
c. Given constant P, ΔP = 0, therefore W = - PΔV. Thus ΔH = Q - PΔV + P(ΔV) = Qp. As there might be heat exchange, (c) may or may not hold.

In b), if the volume changes, there is PV work done, and if the temperature is maintained constant, heat must be supplied or released to balance this work.

mjc123 said:
In b), if the volume changes, there is PV work done, and if the temperature is maintained constant, heat must be supplied or released to balance this work.

Thank you for your reply. I see. So in (b), it could be like an isothermal process, where ΔT = 0 (thus ΔE = 0) but Q ≠ 0.

## 1. What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are related by the formula PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. An ideal gas does not have any intermolecular forces between its particles, and its particles have negligible volume compared to the volume of the gas.

## 2. What is the ideal gas law?

The ideal gas law is a formula that describes the relationship between pressure, volume, temperature, and moles of an ideal gas. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. This law is derived from combining the gas laws of Boyle, Charles, and Avogadro.

## 3. How does temperature affect an ideal gas?

According to the ideal gas law, as the temperature of an ideal gas increases, its volume also increases, assuming pressure and moles remain constant. This is because the particles of an ideal gas have more kinetic energy at higher temperatures, causing them to move faster and take up more space.

## 4. What is the difference between ideal gas and real gas?

An ideal gas is a theoretical gas that follows the ideal gas law perfectly, while a real gas deviates from the ideal gas law at high pressures and low temperatures. This is because real gases have intermolecular forces between their particles and their particles have non-negligible volumes, which affect the pressure, volume, and temperature relationships described by the ideal gas law.

## 5. How is the ideal gas law used in thermodynamics?

The ideal gas law is used in thermodynamics to calculate the work, heat, and internal energy of a gas system. It is also used to determine changes in these properties during thermodynamic processes, such as isothermal, adiabatic, and isobaric processes. The ideal gas law is an important tool for understanding and analyzing the behavior of gases in thermodynamic systems.

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