A pressure cooker is a pot that cooks food much faster than ordinary pots by maintaining a higher pressure and temperature during cooking. The pressure inside the pot is controlled by a pressure regulator (the petcock) that keeps the pressure at a constant level by periodically allowing some steam to escape, thus preventing any excess pressure buildup. Pressure cookers, in general, maintain a gage pressure of 2 atm (or 3 atm absolute) inside. Therefore, pressure cookers cook at a temperature of about 133°C instead of 100°C, cutting the cooking time by as much as 70 percent while minimizing the loss of nutrients. The newer pressure cookers use a spring valve with several pressure settings rather than a weight on the cover.
A certain pressure cooker has a volume of 6 L and an operating pressure of 75 kPa gage. Initially, it contains 1 kg of water. Heat is supplied to the pressure cooker at a rate of 500 W for 30 min after the operating pressure is reached. Assuming an atmospheric pressure of 100 kPa, determine (a) the temperature at which cooking takes place and (b) the amount of water left in the pressure cooker at the end of the process. Answers: (a) 116.04°C, (b) 0.6 kg
(a)
The temperature at which cooking takes place.
Answer to Problem 184RP
The temperature at which cooking takes place is
Explanation of Solution
Write the formula for absolute pressure build up in the cooker.
Here, the absolute pressure is
When the pressure cooker reaches it maximum pressure, the petcock valve allows the steam to exit the cooker, the condition of exit steam is saturated vapor.
Hence, the cooking temperature
Conclusion:
Substitute
Refer Table A-5, “Saturated water-Temperature table”.
The saturation temperature corresponding to the pressure of
Thus, the temperature at which cooking takes place is
(a)
The amount water left in the pressure cooker at the end of the process.
Answer to Problem 184RP
The amount water left in the pressure cooker at the end of the process is
Explanation of Solution
Write the equation of mass balance.
Here, the inlet mass is
The change in mass of the system for the control volume is expressed as,
Here, the suffixes 1 and 2 indicates the initial and final states of the system.
Consider the given pressure cooker as the control volume.
Initially the cooker is filled with liquid and vapor and further no other mass is allowed to enter the cooker. Hence, the inlet mass is neglected i.e.
Rewrite the Equation (I) as follows.
At initial state:
There is saturated mixture of water present in the pressure cooker.
Write the formula of initial specific volume
Here, the volume of pressure cooker is
Write the formula for quality of mixture at initial state.
Write the formula for internal energy of steam at initial state.
Here, the specific volume is
Write the energy balance equation.
Here, the heat transfer is
Since the pressure cooker is not insulated, the heat transfer occurs through the pressure cooker wall. In control volume, there is no work transfer, i.e.
The Equation (V) reduced as follows.
Write the formula for amount of heat supplied to the cooker.
Here, the rate of heat supply is
Consider, at final state the pressure cooker consist of saturated mixture.
Write the formula for specific volume
Write the formula for internal energy
Write the formula for mass of steam
Here, the subscript 2 indicates the final state.
The properties of the steam at both initial and final states are equal, the only variation occurs with their quality.
The pressure cooker consist of mixture of vapor
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following corresponding to the pressure of
The initial fluid and gaseous specific volume is as follows.
The initial fluid and gaseous internal energy is as follows.
When the pressure cooker reaches it maximum pressure, the steam starts to exit the cooker, the condition of exit steam is saturated vapor.
Hence, the exit enthalpy
Conclusion:
Substitute
Substitute
Substitute
Equation (VI).
Substitute
Substitute
Equation (X).
Substitute
Substitute
Substitute
Substitute
Use Engineering Equation Solver (EES) or online calculator to solve the Equation (XIV) and obtain the value of
Substitute
Thus, the amount water left in the pressure cooker at the end of the process is
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Chapter 5 Solutions
Thermodynamics: An Engineering Approach
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