To what temperature, in kelvins, must the tank be cooled from its initial state

Question

To what temperature, in kelvins, must the tank be cooled from its initial state to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)?

A.What is the final pressure, in pascals, in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?

B.What is the final pressure, in pascals, if one-tenth of the gas escapes during this process?

C.To what temperature, in kelvins, must the tank be cooled from its initial state to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)?

Explanation / Answer

given data

volume =50 L

Pressure = 1.5*10^7 N/m^2

temperature of 25°C

T2 = 273-78.5 = 194.5K

T1 = 273 + 25 = 298K

(a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?

from ideal gas equation

P = P (T/ T) /since volume is constant.

P = 1.55*10^7* (194.55/ 298) = 1.01*10^7 Pa

B.What is the final pressure, in pascals, if one-tenth of the gas escapes during this process?

The pressure will be reduced to 0.9 P = 0.909*10^7 Pa

C.To what temperature, in kelvins, must the tank be cooled from its initial state to reduce

the pressure to 1.00 atm

P/ T = P /T since volume is constant.

1.01325*10^5/ T = 1.55*10^7 / 298

T = 1.94 K
T = -271.06° C

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