A sample of oxygen gas at 25.0°c has its pressure tripled while its volume is halved. What is the final temperature of the gas?
2 answers:
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The gas is in a rigid container: this means that its volume remains constant. Therefore, we can use Gay-Lussac law, which states that for a gas at constant volume, the pressure is directly proportional to the temperature. The law can be written as follows:
Where P1=5 atm is the initial pressure, T1=254.5 K is the initial temperature, P2 is the new pressure and T2=101.8 K is the new temperature. Re-arranging the equation and using the data of the problem, we can find P2:
So, the new pressure is 2 atm.
To solve this problem we will apply the concepts related to the Area, the power and the proportionality relationships between intensity and distance.
The expression for sound power is,
Here,
A = Area
I = Intensity
P = Power
At the same time the area can be written as,
Now the intensity is inversely proportional to the square of the distance from the source, then
The expression for the intensity at different distance is
Here,
= Intensity at distance 1
= Intensity at distance 2
= Distance 1 from light source
= Distance 2 from the light source
If we rearrange the expression to find the intensity at second position we have,
If we replace with our values at this equation we have,
Now using the equation to find the area we have that
Finally with the intensity and the area we can find the sound power, which is
Power is defined as the quantity of Energy per second, then