Solving for Pressure Inside a Sealed Syringe
What is the pressure inside the syringe when the volume of air is reduced to 10 ml?
You fill a syringe with 50 ml of air at normal atmospheric pressure (0.95 atm). After sealing the syringe, you push the plunger to a position corresponding to inside volume of 10 ml. What is the pressure inside the syringe?
Pressure Inside the Sealed Syringe:
The pressure inside the sealed syringe, when the volume of air is reduced to 10 ml, is 4.75 atm.
The question can be addressed using Boyle's Law in physics which provides the relationship between pressure and volume of a gas. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature and quantity are held constant.
To solve for the pressure inside the sealed syringe, we can use the formula derived from Boyle's Law: P1V1 = P2V2. Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
In this scenario, the initial pressure (P1) is 0.95 atm, the initial volume (V1) is 50 ml, and the final volume (V2) is 10 ml. By substituting these values into the formula and solving for P2, we find that the pressure inside the syringe is 4.75 atm when the volume of air is reduced to 10 ml.
Explanation:This problem can be solved using the principle of Boyle's Law in physics, which addresses the inverse relationship between the pressure and volume of a gas when temperature and quantity are held constant.
Boyle's Law can be expressed using the formula P1V1 = P2V2 where P1 = initial pressure, V1 = initial volume, P2 = final pressure, and V2 = final volume.
In your case, P1 is 0.95 atm (the initial atmospheric pressure), V1 is 50 ml (the initial volume of air in the syringe), and V2 is 10 ml (the reduced volume after sealing and pushing the plunger).
Following the steps of Boyle's law, you rearrange the equation to find P2: P2 = P1V1 / V2. To find P2, substitute the known values into the equation to obtain: P2 = (0.95 atm * 50 ml) / 10 ml = 4.75 atm. Therefore, the pressure inside the syringe when the volume of air has been reduced to 10 ml is 4.75 atm.