Final answer:
Using the combined gas law, the new pressure in the tank after withdrawing 39% of the gas and increasing the temperature to 54°C is calculated to be approximately 22.12 atm.
Step-by-step explanation:
Calculating the New Pressure in a Gas Tank
To calculate the new pressure in the tank after withdrawing 39 percent of the gas and increasing the temperature, we can use the combined gas law which relates the pressure, volume, and temperature of a gas. The combined gas law is given by:
P1 * V1 / T1 = P2 * V2 / T2
where:
- P1 and P2 are the initial and final pressures.
- V1 and V2 are the initial and final volumes.
- T1 and T2 are the initial and final temperatures in Kelvin.
We were told that the initial pressure (P1) is 12 atm, the initial temperature (T1) is 18°C (which is 291.15 K), and 39% of the gas is withdrawn. If 39% of the gas is removed, the remaining volume of gas will be 61% of the original, since pressure and volume are directly proportional when the amount of gas and temperature are kept constant. We also need to convert the final temperature (T2) of 54°C to Kelvin, which is 327.15 K.
Substituting the values we have:
P2 = P1 * (V1/V2) * (T2/T1)
Since V1/V2 is the ratio of the initial to final volume of gas (which is 1/0.61 because 39% of the gas has been removed), we get:
P2 = 12 atm * (1/0.61) * (327.15 K / 291.15 K)
Calculating this gives us:
P2 = 12 atm * 1.63934 * 1.12368
P2 = 12 atm * 1.84297
P2 ≈ 22.12 atm
Therefore, the new pressure in the tank after withdrawing 39 percent of the gas and raising the temperature to 54°C is approximately 22.12 atm.