An amount of ideal gas is placed in a sealed rigid cylinder. The container is
initially placed in boiling water. It is quickly removed and placed in ice-water bath.
Draw this thermodynamic process on a PV diagram.
If the question change to An amount of ideal gas is in a cylinder with a piston which can move freely
without friction. The gas is slowly heated on a stove. Draw the process on a PV diagram.
In both scenarios, we can use a PV (pressure-volume) diagram to represent the thermodynamic process. In a PV diagram, the x-axis represents volume (V) and the y-axis represents pressure (P).
1. Ideal gas in a sealed rigid cylinder:
In this scenario, the gas is initially placed in boiling water and then quickly removed and placed in an ice-water bath.
- Start by drawing an initial state point (A) on the PV diagram at a certain pressure (P1) and volume (V1).
- Since the container is sealed and rigid, the volume remains constant throughout the process, so draw a vertical line from point A to point B at the same volume but at a different pressure (P2).
- Point B represents the state of the gas when it is removed from boiling water and placed in the ice-water bath.
- Finally, draw another vertical line from point B to point C at the same volume but at a different pressure (P3). Point C represents the state of the gas in the ice-water bath.
- Connect points A, B, and C to complete the process on the PV diagram.
2. Ideal gas in a cylinder with a piston:
In this scenario, the gas in the cylinder is slowly heated on a stove.
- Start by drawing an initial state point (A) on the PV diagram at a certain pressure (P1) and volume (V1).
- As the gas is slowly heated on the stove, it expands, causing an increase in volume. Draw a curve from point A to point B, representing the expansion of the gas.
- Point B represents the state of the gas after it has been heated.
- Finally, draw a vertical line from point B to point C at the same volume but at a different pressure (P2). Point C represents the final state of the gas.
- Connect points A, B, and C to complete the process on the PV diagram.
Please note that the specific values of pressure, volume, and temperature are not provided in the question, so the diagram is just a general representation of the process.
To draw the thermodynamic processes on a PV (Pressure-Volume) diagram, we need to understand the properties of the gas and the changes it undergoes during each process.
1. Boiling water to ice-water bath:
- Initially, the gas is in a container placed in boiling water, so it undergoes an isothermal expansion. During an isothermal expansion, the temperature remains constant while the volume increases.
- On a PV diagram, an isothermal process is represented by a horizontal line since the pressure and volume change but the temperature remains constant.
- Draw a horizontal line from the initial point (representing the initial pressure and volume) towards the right to represent the expansion.
2. Slow heating on a stove:
- In this process, the gas is slowly heated on a stove, which causes it to expand. Since the expansion is slow, it can be assumed to be quasi-static.
- A quasi-static process is an idealized process where the system is always in thermal equilibrium. In this case, the temperature and pressure of the gas increase gradually, corresponding to an increase in volume.
- On a PV diagram, a quasi-static process is represented by a curved line that starts from the initial point and moves towards higher pressures and volumes.
Note: The direction of the curve depends on the specific characteristics of the gas and the stove. If the gas follows the ideal gas law, the curve will be an upward-sloping curve towards the right. However, if the gas undergoes non-ideal behavior or if the heat source causes the gas to cool instead of expand, the curve may have a different shape.
It's important to note that without specific values for temperature, pressure, and volume, the specific shape of the curves cannot be accurately determined, but the general trends can be illustrated.