If 4.5 m3 of a gas initially at STP is compressed to 2.6 m3 and the temperature is raised to 33oC, what is the new pressure?
If P is in atm, then
2.6P/(33+273) = 4.5*1/273
Well, let me tell you, this gas really knows how to handle pressure! So, we know that the initial volume of the gas is 4.5 m3, and it gets compressed to 2.6 m3. That's quite a squeeze! Now, as for the temperature, it rises to 33oC. This gas must really like hot weather!
To find the new pressure, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Since we're dealing with the same gas, the number of moles, gas constant, and temperature all remain constant. So, we can simplify the ideal gas law to P1V1 = P2V2.
Using that equation, we can plug in the values. P1 is the initial pressure, V1 is the initial volume, P2 is the new pressure, and V2 is the new volume. Let's do the math and find out what the new pressure is!
P1V1 = P2V2
P2 = (P1V1) / V2
Now we just plug in the values we know. P1 is the pressure at STP, which is approximately 1 atmosphere. V1 is 4.5 m3, and V2 is 2.6 m3. Let's work it out!
P2 = (1 atm * 4.5 m3) / 2.6 m3
And the final answer is... drumroll, please... Ta-da! The new pressure is approximately 1.73 atmospheres. So, this gas really knew how to handle the pressure and the heat!
To find the new pressure of the gas, we can use the combined gas law. The combined gas law states that the product of the initial pressure and initial volume divided by the initial temperature is equal to the product of the final pressure and final volume divided by the final temperature. The equation is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we want to find)
V2 = final volume (given as 2.6 m3)
T2 = final temperature (given as 33oC)
Let's plug in the values we have:
(P1 * 4.5 m3) / 273 K = (P2 * 2.6 m3) / (33 + 273) K
Now we can solve for P2, the final pressure:
(P1 * 4.5) / 273 = (P2 * 2.6) / 306
To isolate P2, the final pressure, we can cross-multiply:
(P1 * 4.5 * 306) = (P2 * 2.6 * 273)
Now we can divide both sides by (2.6 * 273):
(P1 * 4.5 * 306) / (2.6 * 273) = P2
To find the specific value for P2, you'll need to know the initial pressure (P1). If you have that information, you can substitute that value into the equation and solve for P2.