How Does the Ideal Gas Law Solve Temperature and Volume Changes in Gases?

[mustang]

Problem1. A cylinder with a movable piston contains gas at a temperature of 42 degrees Celicius, with a volume of 40m^3 and a pressure of 0.233*10^5 Pa.
What will be the final temperature of the gas if it is compressed to 0.728 m^3 and its pressure is increaded to 0.609*10^5 Pa? Answer in K.
How is this done?

Problem 3.
A gas bubble with a volume of 0.14 cm^3 is formed at the bottom of a 11.1 cm deep container of merccury. The temperature is 24 degrees Celisius at the bottom of the container and 43 degees Celisuis at the top of the container.
The acceleration of gravity is 9.81 m/s^2.
What is the volume of the bubble just beneath the surface of the mercury? Assume that the surface is at atmospheric pressure.
Answer in units of m^3.
How is correctly done?

 

[Doc Al]

Well? Where are you stuck? Show what you've done. Start by stating the ideal gas law.

 

[mustang]

Problem 3.

For problem what formula would you use?
We only the IDeal Gas Formula :P V = n R T
P is the pressure, V is the volume, n is the number of mols of gas, T is the absolute temperature, and R is the Universal Gas Constant.
If this is a good formula to do this problem can you show your steps, step-by-step.

 

[Doc Al]

Problem 3

Right, you would use the ideal gas law. Since n is a constant (the number of gas atoms doesn't change), I would rewrite it as PV/T = constant. Now compare the values for two points: (1) at the bottom of the mercury column and (2) near the top:
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$
You have to solve for V2, by plugging in the values for the other variables. You'll have to figure out the pressure at the bottom of that column of mercury, for one! At the top, just assume it's atmospheric pressure.

Give it a shot.

 

[mustang]

Right, you would use the ideal gas law. Since n is a constant (the number of gas atoms doesn't change), I would rewrite it as PV/T = constant. Now compare the values for two points: (1) at the bottom of the mercury column and (2) near the top:
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$
You have to solve for V2, by plugging in the values for the other variables. You'll have to figure out the pressure at the bottom of that column of mercury, for one! At the top, just assume it's atmospheric pressure.

Give it a shot.

What would the values of the pressures be if they give you just the volumes and temperatures?

 

[Doc Al]

pressures are given

What would the values of the pressures be if they give you just the volumes and temperatures?

I don't understand your question. In this problem you are given all the information needed to figure out the pressures.