A gas in a cylinder is held at a constant pressure of 1.80 * 10^5 Pa and is cooled and compressed from 1.70 m^3 to 1.20 m^3. The internal energy of the gas decreases by 1.40 * 10^5 J. (c) Does it matter whether the gas is ideal? Why or why not?

Verified step by step guidance

1. Identify the type of process: Since the pressure is constant, this is an isobaric process.
2. Understand the work done by the gas: In an isobaric process, the work done by the gas can be calculated using the formula $W = P \Delta V$, where $P$ is the pressure and $\Delta V$ is the change in volume.
3. Relate the change in internal energy to heat transfer: According to the first law of thermodynamics, $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.
4. Consider the characteristics of an ideal gas: For an ideal gas, the internal energy changes are dependent only on temperature changes and not on pressure or volume directly. The heat capacity at constant pressure can be used to relate the change in temperature to the heat added or removed.
5. Evaluate the relevance of the gas being ideal: Since the problem involves changes in volume, pressure, and internal energy, knowing whether the gas behaves ideally helps in simplifying calculations using ideal gas laws and assumptions. If the gas is not ideal, factors like non-ideal interactions and deviations from the ideal gas law at high pressures or low temperatures might need to be considered.

Key Concepts

Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law assumes that gas particles do not interact and occupy no volume, which simplifies calculations but may not hold true for real gases under certain conditions.

Internal Energy

Internal energy is the total energy contained within a system, including kinetic and potential energy of the particles. For an ideal gas, the internal energy depends primarily on temperature, as the potential energy is negligible. In the context of the question, a decrease in internal energy indicates that the gas is losing energy, which can occur through work done on the gas or heat transfer.

Real vs. Ideal Gases

Real gases deviate from ideal behavior due to intermolecular forces and the volume occupied by gas particles, especially at high pressures and low temperatures. Understanding whether a gas behaves ideally is crucial for accurately predicting its behavior during processes like compression and cooling. In this scenario, knowing if the gas is ideal helps determine if the internal energy change can be solely attributed to temperature changes or if other factors must be considered.