A mixture of gasoline vapor and air is placed in an engine cylinder. The piston has an area of 7.4*10^-3 m^2 and is displaced inward by 7.2*10^-2 m. If 9.5*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?
I don't get this at all.
Pressure*Volume= work
Work is being done on the gas mixture: it is being compressed.
Well, if you're feeling a bit lost, don't worry, I'm here to bring some laughter to the world of physics! Let's break down this problem, shall we?
To find the work done, we use the formula:
Work = (Pressure * Area) * Displacement
Now, let's plug in the given values. We have:
- Pressure = 9.5 * 10^5 Pa
- Area = 7.4 * 10^(-3) m^2
- Displacement = 7.2 * 10^(-2) m
So, putting it all together:
Work = (9.5 * 10^5 Pa) * (7.4 * 10^(-3) m^2) * (7.2 * 10^(-2) m)
Now, let's do some math. And remember, kids, stay positive... unless you're a proton!
Work = 49.14 Joules
So, work done during this process is approximately 49.14 Joules. Ah, the wonders of physics!
And as for the direction of work, in this case, work is being done on the gas mixture. It's like squeezing a balloon and compressing it. That poor gas mixture sure is getting a workout, huh?
I hope that puts a smile on your face, and helps you make sense of this problem! If you have any more questions, feel free to ask. Now go out there and conquer the world of physics with a chuckle!
To calculate the work done during the process, we can use the formula:
Work = Pressure * Change in Volume
The given pressure is 9.5 * 10^5 Pa, and the change in volume is determined by the displacement of the piston, which is given as 7.2 * 10^-2 m.
First, let's calculate the change in volume:
Change in Volume = Area * Displacement
= (7.4 * 10^-3 m^2) * (7.2 * 10^-2 m)
Multiplying these values:
Change in Volume = 5.328 * 10^-4 m^3
Now we can calculate the work:
Work = Pressure * Change in Volume
= (9.5 * 10^5 Pa) * (5.328 * 10^-4 m^3)
Multiplying these values:
Work = 5.0576 * 10^2 J
So, the work done during this process is approximately 505.76 J.
Now regarding whether work is being done on or by the gas mixture, since the piston is displaced inward, the gas mixture is being compressed. Therefore, work is being done on the gas mixture.
To calculate the work done in this process, we can use the formula:
Work = Pressure * Change in Volume
Let's break it down step by step:
1. Calculate the change in volume:
The piston is displaced inward by 7.2*10^-2 m. This means that the volume decreases by this amount, so we have:
Change in Volume = -7.2*10^-2 m
Note: The negative sign indicates a decrease in volume.
2. Substitute the values into the formula:
Work = 9.5*10^5 Pa * (-7.2*10^-2 m)
3. Calculate the work:
Multiply the pressure (-7.2*10^-2 m) by the change in volume (-7.2*10^-2 m):
Work = -6.84*10^4 J
The negative sign indicates that work is being done on the gas mixture. The gas mixture is compressed, and energy is transferred to it in the form of work.
Therefore, the work done during this process is -6.84*10^4 J (joules), and the work is being done on the gas mixture.