What is the relationship between the number of particles and temperature, when the pressure and volume are held constant? As addition of particles are pumped into the particle box, the temperature is dropping with constant pressure and volume. What type of relationship is this: directly proportional or inversely proportional? What type of graph represents this relationship: Sketch a graph. What is the relationship between the temperature and number of particles and volume of the chamber, when the pressure is held constant? The number of gas molecules is directly proportional to the volume of the chamber. What type of relationship is this: directly proportional or inversely proportional? DIRECTLY PROPORTIONAL Sketch a graph that represents this relationship.
The Correct Answer and Explanation is:
When the pressure and volume of a gas are held constant, the relationship between the number of particles (or molecules) and the temperature can be understood through the Ideal Gas Law, which is expressed as: PV=nRTPV = nRTPV=nRT
Where:
- PPP is pressure,
- VVV is volume,
- nnn is the number of particles (or moles of gas),
- RRR is the universal gas constant,
- TTT is the temperature.
In this case, if the pressure PPP and volume VVV are constant, the equation can be simplified to: nT=constantnT = \text{constant}nT=constant
This means that the number of particles (nnn) is inversely proportional to the temperature (TTT) when pressure and volume are constant. As more particles are added to the box (i.e., increasing nnn), the temperature drops, because the equation indicates that if nnn increases, TTT must decrease to maintain a constant value.
Type of Relationship:
The relationship between the number of particles and temperature, when pressure and volume are constant, is inversely proportional. This means that as the number of particles increases, the temperature decreases.
Graph Representation:
The graph for this relationship would show an inverse relationship: as the number of particles (on the x-axis) increases, the temperature (on the y-axis) decreases. This results in a curve that slopes downward, resembling a hyperbola.
Second Case: Relationship Between Temperature, Number of Particles, and Volume (Constant Pressure):
When the pressure is held constant, the relationship between the temperature and the number of particles is influenced by the volume of the chamber. The Ideal Gas Law tells us that: P=nRTVP = \frac{nRT}{V}P=VnRT
Since PPP and VVV are constant, this relationship implies that the number of particles (nnn) is directly proportional to the volume (VVV) when temperature is also constant.
Type of Relationship:
The number of gas molecules and the volume of the chamber are directly proportional. This means that increasing the volume allows more particles to fit into the chamber, and the number of particles increases proportionally with volume, assuming pressure remains constant.
Graph Representation:
The graph for this relationship would show a direct relationship: as the number of particles (on the x-axis) increases, the volume (on the y-axis) increases in a straight line.
Summary:
- Number of particles and temperature (constant pressure and volume):
- Relationship: Inversely proportional.
- Graph: Downward-sloping curve (hyperbolic).
- Number of particles and volume (constant pressure):
- Relationship: Directly proportional.
- Graph: Straight line, sloping upwards.
