A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.00x

Question

A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.00x10^7 N/m^2 and a temperature of 27.0 degrees C. Its valve leeks after the cylinder is dropped. The cylinder is colled to dry ice temperature (-78.5 degrees C), to reduce the leak rate and pressure so that it can be safely repaird.

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? (in N/n^2)

b) What is the final pressure if one-tenth of the gas escapes? (in N/m^2)

c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (in K)

Explanation / Answer

Converting oC to K, first of all.

(a)

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

P = 1.0 x107 (194.65/ 300.15) = 0.6485x107 Pa

b)

The pressure will be reduced to 0.9 P = 5.8365x108 Pa


c)

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


101325/ T = 1.0x107 / 300.15

T = 3.041269875 K
T = -270.108730125 oC

Calculations maybe faulty, logic is correct.

Hope this helps :)

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