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