How to Calculate the New Pressure of a Syringe After Cooling and Compressing?

What is the new pressure of a plastic syringe filled with air particles after being cooled to a temperature of 180 K and compressed to a volume of 1.25 mL? Using the combined gas law (P1V1/T1 = P2V2/T2), and the initial conditions of 4.14 atm pressure, 12.5 mL volume, and 251 K temperature, the final pressure after cooling to 180 K and compressing to 1.25 mL is calculated to be 29.664 atm.

To calculate the new pressure of a syringe after it is cooled and compressed, we need to apply the combined gas law, which relates the pressure, volume, and temperature of a gas. The combined gas law is written as (P1V1/T1) = (P2V2/T2), where P1 and P2 are the pressures, V1 and V2 are the volumes, and T1 and T2 are the temperatures in Kelvin of the states 1 and 2, respectively.

Let's plug in the initial conditions:

  • P1 = 4.14 atm
  • V1 = 12.5 mL
  • T1 = 251 K

And the final conditions:

  • V2 = 1.25 mL
  • T2 = 180 K

Since the initial and final units of volume and pressure are the same, we can directly apply the formula:

P2 = (P1 * V1/T1) * (T2/V2)

P2 = (4.14 atm * 12.5 mL/251 K) * (180 K/1.25 mL)

P2 = (0.206 atm*mL/K) * (144 K/mL)

Thus, the new pressure of the syringe after it is cooled to 180 K and compressed to 1.25 mL is 29.664 atm.

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