Pressure-volume work (formula for work) (article) | Khan Academy
The Relationship between Pressure and Volume: Boyle's Law Because PV is a constant, decreasing the pressure by a factor of two results in. Discuss the relationship between present value and future value If there are multiple payments, the PV is the sum of the present values of each payment and . Another way to describing it is saying that their products are constant. PV = C Gives the relationship between volume and amount when pressure and.
In a gasoline engine, the pressure inside the piston changes when the fuel is combusted inside the piston, releasing thermal energy and causing the volume inside the piston to increase.
The volume inside the piston decreases when the gas is allowed to escape from the piston. As that process is repeated, your wheels can move!
If the gas is heated, energy is added to the gas molecules. We can observe the increase in average kinetic energy of the molecules by measuring how the temperature of the gas increases.
As the gas molecules move faster, they also collide with the piston more often. These increasingly frequent collisions transfer energy to the piston and move it against an external pressure, increasing the overall volume of the gas. In this example, the gas has done work on the surroundings, which includes the piston and the rest of the universe.
To calculate how much work a gas has done or has done to it against a constant external pressure, we use a variation on the previous equation: Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.
The Pressure Temperature Law This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.
P Same as before, a constant can be put in: The Volume Amount Law Amedeo Avogadro Gives the relationship between volume and amount when pressure and temperature are held constant.
Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract. If the amount of gas in a container is increased, the volume increases.
The Relationship Between Present and Future Value
If the amount of gas in a container is decreased, the volume decreases. V As before, a constant can be put in: The Combined Gas Law Now we can combine everything we have into one proportion: The volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure. Same as before, a constant can be put in: The Ideal Gas Law The previous laws all assume that the gas being measured is an ideal gas, a gas that obeys them all exactly.
The Irish chemist Robert Boyle — carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury, as shown in Figure 6. In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature.
More mercury is then poured into the open arm to increase the pressure on the gas sample. The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately.
This relationship between the two quantities is described as follows: Dividing both sides of Equation 6. The numerical value of the constant depends on the amount of gas used in the experiment and on the temperature at which the experiments are carried out.
At constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure. Boyle used non-SI units to measure the volume in. Hg rather than mmHg.
- 6.3: Relationships among Pressure, Temperature, Volume, and Amount
- The Relationship Between Present and Future Value
Because PV is a constant, decreasing the pressure by a factor of two results in a twofold increase in volume and vice versa. The Relationship between Temperature and Volume: