A welding tank has a gauge pressure of 2000psi at 40.0°F. What is the new gauge pressure if the temperature rises to 100°F?
At constant volume, P/T = constant.
To use this formula, P must be the absolute pressure and T must be absolute (Kelvin or Rankine).
To convert Fahrenheit temperature to Rankine, add 460. The ideal gas law says:
(2000 + 14.7)/(40 + 460)
= (P + 14.7)/(100 + 460)
where P is the final gauge pressure.
14.7 ps1 has been added to gauge pressures to convert to absolute pressure in psia
2014.7/500 = (P + 14.7)/560
P + 14.7 = 2256.4
P = 2241.8 psi is the final gauge pressure.
To solve this problem, you need to use the ideal gas law, which states that the pressure, temperature, and volume of a gas are related. The ideal gas law equation is:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant, and
T is the temperature of the gas in Kelvin.
Before we can use the ideal gas law, we need to convert the temperature from Fahrenheit to Kelvin. The formula to convert Fahrenheit to Kelvin is:
T(K) = (T(°F) + 459.67) * (5/9)
Let's start by converting the initial temperature of 40.0°F to Kelvin:
T1(K) = (40.0 + 459.67) * (5/9)
T1(K) = 277.59 K
Next, we need to convert the final temperature of 100°F to Kelvin:
T2(K) = (100 + 459.67) * (5/9)
T2(K) = 310.93 K
Now, we can set up a proportion using the initial and final temperatures to find the new pressure.
(P1 / T1) = (P2 / T2)
We know the initial pressure (2000 psi) and the initial and final temperatures (T1 = 277.59 K and T2 = 310.93 K). We need to solve for P2, the new pressure.
Let's plug in the values into the equation and solve for P2:
(2000 psi / 277.59 K) = (P2 / 310.93 K)
Cross-multiplying the equation gives:
2000 psi * 310.93 K = 277.59 K * P2
621,860 psi-K = 277.59 K * P2
Now, divide both sides by 277.59 K to isolate P2:
P2 = (621,860 psi-K) / 277.59 K
Calculating this value gives the new gauge pressure:
P2 ≈ 2,238.17 psi
Therefore, the new gauge pressure when the temperature rises to 100°F is approximately 2,238.17 psi.