Two moles of an ideal gas are heated at constant pressure from T = 27°C to T = 107°C. (a) Draw a pV-diagram for this process. (ANSWER IS )

Verified step by step guidance

1. Convert the initial and final temperatures from Celsius to Kelvin by adding 273.15 to each. This is because the ideal gas law and related calculations require temperature in Kelvin.
2. Identify that the process is at constant pressure, which means the pressure (p) does not change. On a pV-diagram, this is represented by a horizontal line.
3. Use the ideal gas law, PV = nRT, to understand how the volume (V) changes with temperature (T) when the number of moles (n) and the gas constant (R) are constant. Since the pressure is constant and the temperature increases, the volume must also increase.
4. Calculate the initial and final volumes using the ideal gas law. Since the pressure is constant, the ratio of volumes is equal to the ratio of temperatures (V2/V1 = T2/T1).
5. Sketch the pV-diagram: Start by plotting the initial state at the calculated initial volume and constant pressure. Then draw a line horizontally to the right to the calculated final volume at the same pressure level, indicating an increase in volume.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law is fundamental in understanding the behavior of gases under various conditions, particularly when analyzing processes like heating or cooling at constant pressure.

Constant Pressure Process

In a constant pressure process, the pressure of the gas remains unchanged while its temperature and volume may vary. This is significant in thermodynamics as it allows for the calculation of work done by or on the gas, and it influences the shape of the pV-diagram, which typically shows a horizontal line for constant pressure.

pV-Diagram

A pV-diagram is a graphical representation of the relationship between pressure (p) and volume (V) for a gas. In this diagram, the area under the curve represents work done during the process, and the shape of the curve can indicate whether the process is isothermal, isobaric, or adiabatic, providing insights into the thermodynamic behavior of the gas.