A mixture of gasoline vapor and air is placed in an engine cylinder. The piston has an area of 7.4 x 10^-3 m^2 and is displaced inward by 7.2 x 10^-2 m. If 9.5 x 10^5 Pa of pressure is placed on the piston, how much work is done during this process? Is work being done on or by the gas mixture?
Well, it seems like the gasoline and air mixture really had some pressure on it! Let's see how much work was done during this process.
Work (W) is given by the formula: W = force × distance.
The force exerted on the piston can be calculated using the formula: force = pressure × area.
Plugging in the values, we have:
force = (9.5 x 10^5 Pa) × (7.4 x 10^-3 m^2).
Now, let's calculate the force first:
force = 7.03 N.
The distance the piston was displaced inward is given as 7.2 x 10^-2 m.
Now, we can calculate the work done by using the formula:
W = force × distance.
Plugging in the values, we get:
W = (7.03 N) × (7.2 x 10^-2 m).
Calculating it out:
W = 0.505 N·m.
Now, to answer your second question, work is being done on the gas mixture. In this case, the force is applied on the piston to compress the gas, resulting in work done on the gas mixture.
So, to sum it up, the work done on the gasoline and air mixture is 0.505 N·m. Keep up the good work with your questions!
To calculate the work done on or by the gas mixture, we can use the formula:
Work = Force * Distance
First, let's calculate the force exerted on the piston:
Force = Pressure * Area
Given that the pressure is 9.5 x 10^5 Pa and the area is 7.4 x 10^-3 m^2, we can substitute these values into the formula:
Force = (9.5 x 10^5 Pa) * (7.4 x 10^-3 m^2)
Next, calculate the work done by the gas mixture:
Work = Force * Distance
Given that the distance is 7.2 x 10^-2 m, we can substitute the values into the formula:
Work = (Force) * (7.2 x 10^-2 m)
Now, let's substitute the calculated force into the formula:
Work = [(9.5 x 10^5 Pa) * (7.4 x 10^-3 m^2)] * (7.2 x 10^-2 m)
Calculating this expression will give us the value of work done during the process.
To calculate the work done by or on the gas mixture, you can use the formula:
Work = Force x Distance
First, let's find the force exerted on the piston. The force can be calculated using the equation:
Force = Pressure x Area
Given:
Pressure = 9.5 x 10^5 Pa
Area = 7.4 x 10^-3 m^2
Calculating the force:
Force = 9.5 x 10^5 Pa x 7.4 x 10^-3 m^2
Force = 7.03 N
Now, let's find the distance or displacement.
Distance = 7.2 x 10^-2 m
Using the calculated force and distance, we can find the work done:
Work = Force x Distance
Work = 7.03 N x 7.2 x 10^-2 m
Work = 0.506 J
So, the work done during this process is 0.506 Joules.
To determine whether the work is done on or by the gas mixture, we need to consider the sign of the work. If the work is positive, it means work is done by the gas mixture (work output). If the work is negative, it means work is done on the gas mixture (work input).
In this case, if the cylinder is being compressed (piston is moving inward), it means work is being done on the gas mixture, so the work done is negative.