1. An ideal gas at 40psig and 80 degree F is heated in a closed container to 120 degree F. What is the final pressure, psia?
Convert 80 F and 120 F to C.
Convert 40 psig to psia. 40+14.7 = ? psia.
Then (P1/T1) = (P2/T2) and solve for P2. P2 will be in psia.
Don't forget to convert C (after you've converted F to C) to Kelvin.
K = 273.15 + C
If this is an engineering problem you can use Rankin
To solve this problem, we will use the ideal gas law equation:
PV = nRT
Where:
P = Pressure of the gas (in this case, initially 40 psig)
V = Volume of the gas (constant since it is in a closed container)
n = Number of moles of the gas (constant if the amount of gas remains the same)
R = Ideal gas constant (constant)
T = Temperature of the gas in Kelvin
To convert the initial pressure from psig (pound-force per square inch gauge) to psia (pound-force per square inch absolute), we add the atmospheric pressure. Atmospheric pressure is around 14.7 psi. Therefore, the initial pressure in psia is:
Initial Pressure (psia) = Initial Pressure (psig) + Atmospheric Pressure
Now, let's calculate the initial pressure in psia:
Initial Pressure (psia) = 40 psig + 14.7 psi
Initial Pressure (psia) = 54.7 psia
Next, we need to convert the temperatures to Kelvin:
Initial Temperature (Kelvin) = (80°F + 459.67) * 5/9
Initial Temperature (Kelvin) = 299.82 K
Final Temperature (Kelvin) = (120°F + 459.67) * 5/9
Final Temperature (Kelvin) = 322.04 K
Now, we can rearrange the ideal gas law equation to solve for the final pressure:
P_final = (P_initial * V * T_final) / (V * T_initial)
Since the volume (V) and number of moles (n) are constant, they cancel out:
P_final = (P_initial * T_final) / T_initial
Plugging in the values:
P_final = (54.7 psia * 322.04 K) / 299.82 K
Calculating the final pressure:
P_final = 58.93 psia
Therefore, the final pressure in psia is approximately 58.93 psia.