Hello, Miracle,
There is a set of gas laws that cover these types of questions. It is a pain to remember the names and formulas for each, so I'll give you my technique after answering your specific question.
The change in gas pressure as a function of temperature is given by Gay-Lussac's law. There is no mention of a volume change, so we must assume it is constant. And no gas added or removed. Under those conditions, one expects that as you raise the temperature, the pressure will go up.
The formula is simple: P1/T1 = P2/T2, where T1 and P1 are the initial conditions, and T2 and P2 are the final conditions. One important feature in the gas is that all temperatures must be absolute, or on the Kelvin scale. Remember that Kelvin = 273 + C.
Let's rearrange the formula so that we can isolate the value we are looking for.:
P2 = P1*(T2/T1)
Make a table. I entered everything but P2 and then used the equation for P2. The pressure increased by 11 Pascal, whoever he is. Note that all the temperatures were converted to Kelvin before entering.
P1 312 Pa
T1 305 K
P2 ? Pa
T2 213 K
The result is 323 Pascal, whoever he is.
I hope this helps,
Bob
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I promised a technique that helps remember the gas laws. Here it is.
First, here are the other three main laws: I hope you'll understand and be sympathetic, there are just too many laws for me to remember which is which and whose is whose.
Charles' Law
Boyle's Law
Gay-Lussac's Law: was covered in the problem.
Avogadro's Law
These individual laws lead to a combined gas law that is important to remember:
PV = nRT
P is the pressure, V is volume, n is moles of gas, R is the gas constant, and T is the absolute temperature(K).
Remember "PV = nRT." It has a nice ring to it once you repeat it several times.
Drum roll: The technique I always use when given a gas problem involving changes of conditions only (gas neither added nor removed) is to remember the following:
P1V1/T1 = P1P2/T2
The "1" and "2" subscripts are the initial and final values. Super easy and gets rid of the pesky n (moles) and gas constant (R), because they don't change. It is simply the division of two PV = nRT equations and rearranging so that I can remember it. As long as no gas enters or leaves, this can be used for all gas problems, instead of trying to remember 3 different relationships. Say it aloud a few times, and it is easy to remember. P1, V1, over T1 equals P2, V2 over T2.
Have fun,
Bob
