Rate of pressure increase of contained air being heated

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SUMMARY

The discussion centers on the behavior of air pressure in a sealed steel tank when heated from 0°C to higher temperatures (100°C, 200°C, and 300°C). According to the ideal gas law (PV=nRT), the pressure is directly proportional to the temperature, with the absolute pressure starting at approximately 100 kPa (1 atmosphere). It is emphasized that in a rigid tank, the volume remains constant, and thus the pressure increase is solely dependent on the temperature change. Air can be treated as an ideal gas under these conditions, provided there is minimal water vapor present.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of thermodynamic temperature and conversions (Celsius to Kelvin)
  • Familiarity with the concept of absolute pressure
  • Basic principles of gas behavior under varying temperatures
NEXT STEPS
  • Research the implications of the ideal gas law on pressure changes in rigid containers
  • Explore the concept of absolute pressure versus gauge pressure
  • Investigate the behavior of gases at high temperatures and pressures
  • Learn about the effects of humidity on gas behavior and ideal gas assumptions
USEFUL FOR

Engineers, physicists, and anyone interested in thermodynamics, particularly those working with gas systems and pressure management in sealed environments.

hjb39
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Wondering if I have a sealed steel tank filled with air and the air temp is 0C and the air pressure in the tank is 0, then heat is applied to the tank - what will the pressure be 100C? At 200C? At 300C? I assume the rate of expansion is constant, but correct me if this is wrong. Thanks.
 
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Are you familiar with the ideal gas law: ##PV=nRT##. It states (among other things) that the pressure is directly proportional to the temperature.

A brief note about the quantities: ##P## is the absolute pressure. So what you call 0 pressure is actually 1 atmosphere pressure or about 100 kPa. Also, the T is thermodynamic temperature measured in Kelvin. So 0 C is 273 K.
 
hjb39 said:
I assume the rate of expansion is constant
Careful. There is no "expansion" if the tank is rigid. It's the P part of @Dale 's formula that counts. V would be constant.
I suggest you google "Gas Laws" and search around for a link that makes sense to you. There will be a range of difficulty in the hits you get.
But Air is pretty well behaved at the temperatures you quote and you can treat it as a 'ideal gas' as long as you make sure there's very little water vapour.
 
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