In a pressure cooker I start with temperature of 70 degree F

In a pressure cooker I start with temperature of 70 degree F and a pressure of 1 atm. What pressure will be in the cooker if I measure a temperature of400 degree F? Assume I still have cooking beans and water in the cooker. What will be the value of quality?

Solution

According to the ideal gas equation PV=nRT

were P = pressure of system ( pressure cooker in this condition is stated as system)

V= volume of system

T= temperature of system

n = no of moles of system

R is the universal gas constant

in our system ( pressure cooker ) V, n ,R are constant

so P/T = constant

let (1) be the initial stage and (2) be the boiling stage

thus P₁/T₁ = P₂/T₂ --------------Eqn (1)

P₁= intial pressure = 1 atm =101325N/M²

T₁ = intial temp = 70⁰ F= 294.261 K

T₂ = final temp = 400⁰F = 477.6 K

as per Eqn (1) P₂ = P₁*T₂ / T₁ =(101325 * 477.6) /294.261 = 164455.432 N/M²

therefore pressure at 400⁰F = 1.623 atm

Pressure cooker is a closed system in which only energy is transferd and mass is not transfered

in pressure cooker system by increasing the internal pressure increses the boiling point of water also increase thus more temperature is required for boiling , thus more temperature can be transfered to food items and easily cooked

in open system water boils at 100 degree after that point the heat energy what we given will be only used to convert it from liquid to solid state thus less temperature can be transfered to cooking items   

since pressure cooker is a closed system thus the quantity of beans and water will not be changed ( water change of stat from liquid to gaseous occurs