The instruction booklet for your pressure cooker indicates that its highest setting is 11.4 psi. You know that standard atmospheric pressure is 14.7 psi, so the booklet must mean 11.4 psi above atmospheric pressure. At what temperature will your food cook in this pressure cooker set on "high"?
you have to look at what is the bp of water at 26.1 psi. http://www.engineeringtoolbox.com/boiling-point-water-d_926.html
To determine the cooking temperature in the pressure cooker set on "high," you need to calculate the corresponding absolute pressure. Absolute pressure is the sum of atmospheric pressure and the pressure indicated by the pressure cooker.
Given:
Atmospheric pressure (P_atm) = 14.7 psi
Cooker pressure (P_cooker) = 11.4 psi
To find the absolute pressure (P_abs) inside the pressure cooker:
P_abs = P_atm + P_cooker
P_abs = 14.7 psi + 11.4 psi
P_abs = 26.1 psi
Now, to calculate the corresponding temperature in Fahrenheit (T), we can use the ideal gas law equation:
PV = nRT
Where:
P = Absolute pressure
V = Volume
n = Number of moles of gas (assumed constant)
R = Ideal gas constant
T = Temperature in Kelvin
Since we are assuming a constant volume, we can rewrite the ideal gas law equation as:
P = nRT
Now, let's convert the pressure from psi to atmospheres (atm) since the ideal gas constant (R) is in atm.
1 atm = 14.7 psi
So, the absolute pressure (P_abs) in atmospheres is:
P_abs_atm = P_abs / 14.7
P_abs_atm = 26.1 psi / 14.7 psi
P_abs_atm = 1.775 atm
Next, let's convert the pressure from atmospheres to Pascals (Pa) since the ideal gas constant (R) is in Pa.
1 atm = 101325 Pa
So, the absolute pressure (P_abs) in Pascals is:
P_abs_Pa = P_abs_atm * 101325 Pa
P_abs_Pa = 1.775 atm * 101325 Pa/atm
P_abs_Pa = 179879.875 Pa
Now, we can rearrange the ideal gas law equation to solve for temperature (T):
T = P / (nR)
Since n (number of moles) and R (ideal gas constant) are constant, we can simplify the equation to:
T = P_abs_Pa / R
The value of the ideal gas constant (R) is approximately 8.314 J/(mol·K).
Now, let's calculate the cooking temperature (T):
T = 179879.875 Pa / 8.314 J/(mol·K)
T ≈ 21617 K
Finally, to convert the temperature from Kelvin (K) to Fahrenheit (°F), we can use the following conversion formula:
T(°F) = (T(K) - 273.15) * 9/5 + 32
T(°F) = (21617 K - 273.15) * 9/5 + 32
T(°F) ≈ 38862.7 °F
Therefore, the food in your pressure cooker set on "high" will cook at approximately 38862.7 °F.
To determine the cooking temperature in a pressure cooker, you need to understand how pressure affects boiling points and use the ideal gas law equation. The ideal gas law equation states:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
In this case, we know the pressure (11.4 psi) and want to find the temperature. However, we need to convert the pressure from psi to a more commonly used unit, such as atmospheres (atm).
1 atm is approximately equal to 14.7 psi. Therefore, the pressure inside the pressure cooker can be calculated as:
Pressure inside cooker = Pressure indicated - Standard atmospheric pressure
Pressure inside cooker = 11.4 psi - 14.7 psi
Pressure inside cooker = -3.3 psi
Now, we can convert the pressure to atmospheres:
1 atm = 14.7 psi
1 atm = 14.7 psi / 1 atm
-3.3 psi = -3.3 psi / 14.7 psi/atm
-3.3 psi = -0.224 atm
Next, we can rearrange the ideal gas law equation to solve for temperature:
T = (PV) / (nR)
Since the volume and the number of moles of gas remain constant during cooking, we can simplify the equation:
T = (P / R) * V / n
Assuming that the volume and the number of moles of gas are constant in your pressure cooker, we can calculate the temperature:
T = (-0.224 atm / R) * V / n
Now, the ideal gas constant (R) is 0.0821 L * atm / (mol * K), and the number of moles (n) and volume (V) will depend on the particular case. Let's assume we have 1 mole of gas and a constant volume of 1 liter for simplicity:
T = (-0.224 atm * L / (mol * K) / (0.0821 L * atm / (mol * K))) * (1 L / 1 mol)
Simplifying the equation:
T = -0.224 / 0.0821 K
T ≈ -2.73 K
It's important to note that negative temperatures are not physically meaningful in this context. The negative sign arises due to the negative pressure difference relative to atmospheric pressure. Therefore, we can ignore the negative sign and conclude that the cooking temperature in the pressure cooker is approximately 2.73 K.
Use the Clausius-Clapeyron equation
ln(P1/P2)=(dHvap/R)(1/T2-1/T1)
Rearrange it and plug in the numbers
P1=26.1 (14.7+11.4)
P2=14.7
dHvap= 40.68 kJ/mol= 40680 J/mol
R= 8.134 J/mol
T1=?
T2= 100C= 373K