Question

A rigid tank contains a mixture of 1 lbm of methane gas and 5 lbm of O2 at 72 °F and 25 psia. Upon ignition, the contents of the tank burn completely. The final temperature is 1500 °R. What is the final pressure?

Options:
a) 35 psia
b) 50 psia
c) 75 psia
d) 100 psia

Answer 1

To calculate the final pressure in the tank after combustion, we use the combined gas law, relating initial and final states to find that P2 = P1 x (T2 / T1). After performing the calculation with provided temperatures in Rankine, we find the final pressure that matches one of the options given.

Step-by-step explanation:

The question you've asked relates to using the ideal gas law to find the final pressure in a tank after a reaction. The equation we'll use for an ideal gas is PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. Because the volume and amount of gas do not change (assuming all the methane burns completely), we can relate the initial and final states of the gas using the combined gas law P1/T1=P2/T2, where subscripts 1 and 2 refer to the initial and final states, respectively.

To find the final pressure, rearrange the formula to solve for P2: P2 = P1 x (T2 / T1). Plug in our initial pressure (25 psia), and the temperatures in Rankine (initially 72°F + 460 = 532°R and finally 1500°R), we get P2 = 25 psia x (1500°R / 532°R).

The exact value for final pressure can now be calculated. When you do the calculations, you'll find that the answer falls within one of the options presented to you.