There are 40 ml of air in a large syringe. With the exit hole plugged, you squeeze the air down to about 10 ml. If the original pressure was 1.0 atmosphere, how much pressure do you need to exert to squeeze it down to 10 ml in atmospheres?
P V = n R T
n stays the same
R stays the same
T stays the same (not really but assume so)
P1 V1 = P2 V2
1 * 40 = P2 * 10
P2 = 4 atm
In real life if you squished it fast it would get hot but assume let cool.
Well, it seems like you're a real "squeeze-master" trying to compress that air! So, let's do the math. We know that the volume goes from 40 ml to 10 ml, which means it gets squeezed to a quarter of its original size. Since Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature, it means that when you squeeze it to 10 ml, the pressure will increase by a factor of 4. Therefore, you'll need to exert a pressure of 4.0 atmospheres to achieve that. Just remember not to pop any balloons in the process!
To determine the pressure exerted to squeeze the air down to 10 ml, you can use Boyle's Law, which states that the initial pressure multiplied by the initial volume equals the final pressure multiplied by the final volume.
Given:
Initial pressure (P1) = 1.0 atmosphere
Initial volume (V1) = 40 ml
Final volume (V2) = 10 ml
Using Boyle's Law equation:
P1 * V1 = P2 * V2
Substituting the given values:
1.0 atm * 40 ml = P2 * 10 ml
Rearranging the equation to solve for P2:
P2 = (1.0 atm * 40 ml) / 10 ml
P2 = 4.0 atm
Therefore, you need to exert a pressure of 4.0 atmospheres to squeeze the air down to 10 ml.
To calculate the pressure exerted to squeeze the air down to 10 ml, we can use Boyle's Law, which states that the pressure and volume of a confined gas are inversely proportional. The formula to express this relationship is:
P1 * V1 = P2 * V2
Where:
P1 is the initial pressure (1.0 atmosphere),
V1 is the initial volume (40 ml),
P2 is the final pressure (which we need to determine), and
V2 is the final volume (10 ml).
We can rearrange the formula to solve for P2:
P2 = (P1 * V1) / V2
P2 = (1.0 atm * 40 ml) / 10 ml
P2 = 40/10
P2 = 4.0 atmosphere
Therefore, you would need to exert a pressure of 4.0 atmospheres to squeeze the air down to 10 ml.