A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.25 × 107 Pa and a temperature of 25.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5°C) to reduce the leak rate and pressure so that it can be safely repaired. 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 1/10 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 there is no leakage during cooling)?
Kinetic Theory of Gas
The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.
P-V Diagram
A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.
A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.25 × 107 Pa and a temperature of 25.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5°C) to reduce the leak rate and pressure so that it can be safely repaired.
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 1/10 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 there is no leakage during cooling)?
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