A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. What type of process is this?

Verified step by step guidance

1. Step 1: Analyze the graph provided. The graph shows pressure (p) on the y-axis and volume (V) on the x-axis. The curve represents the relationship between pressure and volume during the process. The curve is hyperbolic, indicating an inverse relationship between pressure and volume.
2. Step 2: Recognize the type of thermodynamic process. A hyperbolic curve on a p-V diagram typically represents an isothermal process, where the temperature remains constant throughout the process. This is because the product of pressure and volume (pV) remains constant, which is a characteristic of isothermal processes.
3. Step 3: Confirm the process type using the ideal gas law. The ideal gas law is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>V</mi>=<mi>n</mi><mi>R</mi><mi>T</mi></math>. If temperature (T) is constant, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>V</mi></math> remains constant, which matches the behavior shown in the graph.
4. Step 4: Note that the initial temperature of the gas is given as 900°C. However, this temperature does not change during the process if it is isothermal. The temperature remains constant throughout the process.
5. Step 5: Conclude that the process shown in the graph is an isothermal process, based on the hyperbolic shape of the curve and the constant product of pressure and volume.

Key Concepts

Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas, expressed as PV = nRT. This law is fundamental in understanding gas behavior under various conditions and is crucial for analyzing processes involving gases, such as the one depicted in the graph.

Isothermal Process

An isothermal process occurs when a gas expands or compresses at a constant temperature. In the context of the graph, if the temperature remains constant while pressure and volume change, the process can be classified as isothermal, which is characterized by a hyperbolic curve on a pressure-volume graph.

Thermodynamic Processes

Thermodynamic processes refer to the changes in state variables of a system, such as pressure, volume, and temperature. Understanding the type of process (isothermal, adiabatic, isobaric, or isochoric) is essential for analyzing how energy is transferred and transformed in a gas, as illustrated in the provided graph.