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Calculate the pressure in air in a vessel being evacuated, as a function of evacuation time t. The volume of vessel is V and the initial pressure is p`.The process is assumed to be isothermal and the evacuation constant C is independent upon pressure.?
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Calculate the pressure in air in a vessel being evacuated, as a functi...
Calculation of Pressure in an Evacuated Vessel as a Function of Time

Assumptions:
- Isothermal process
- Evacuation constant C is independent of pressure

Pressure as a Function of Evacuation Time:
The pressure in the vessel being evacuated can be calculated using the formula:
\[ p(t) = p' \times e^{-C \times V \times t} \]
- \( p(t) \): Pressure at time t
- \( p' \): Initial pressure in the vessel
- \( C \): Evacuation constant
- \( V \): Volume of the vessel
- \( t \): Evacuation time

Explanation:
- As the vessel is being evacuated, the pressure inside decreases exponentially with time.
- The rate of decrease is determined by the evacuation constant C, volume V, initial pressure p', and evacuation time t.
- The formula is derived from the ideal gas law for an isothermal process, where pressure and volume are inversely proportional.

Significance of Parameters:
- The initial pressure p' determines the starting point of the pressure decrease.
- The evacuation constant C controls the rate at which the pressure decreases.
- The volume V of the vessel affects the overall pressure change.
In conclusion, the pressure in an air vessel being evacuated can be calculated as a function of evacuation time using the provided formula. This equation helps in understanding how the pressure changes over time during the evacuation process.
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Calculate the pressure in air in a vessel being evacuated, as a function of evacuation time t. The volume of vessel is V and the initial pressure is p`.The process is assumed to be isothermal and the evacuation constant C is independent upon pressure.?
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