Thermodynamics HELP: Solving Problems w/ Initial & Final Mass, RMS Speed

[cukitas2001]

Hey I am having some problems with some thermodynamics yet again. Check these out:

1) A welder using a tank of volume V fills it with oxygen (with a molar mass of M) at a gauge pressure of $$p_1$$ and temperature of $$T_1$$. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is $$T_2$$. , the gauge pressure of the oxygen in the tank is $$p_2$$.

A)Find the initial mass of oxygen.
Use R for the ideal gas constant and $$p_a$$ for atmospheric pressure.
B)Find the mass of oxygen that has leaked out.

I know this is a simple one but don't see hwo to set it up. will it be something like the difference of the initial and finals or something? i was tryin to work with the equation pV=nRT

2) Initially, the translational rms speed of an atom of a monatomic ideal gas is 250m/s. The pressure and volume of the gas are each doubled while the number of moles of the gas is kept constant.

What is the final translational rms speed of the atoms?

Well i was looking at the equations for RMS and all require T so how would i got about this problem?

3) The ideas of average and root-mean-square value can be applied to any distribution. A class of 150 students had the following scores on a 100-point quiz:
Score/ Number of Students

10/ 11
20 / 12
30 / 24
40 / 15
50 / 19
60 / 10
70 / 12
80 / 20
90 / 17
100 / 10

A) a asks to find the average score of the class which i ws able to do but part b asks for the root-mean-square of the class...what i tried was something like (10*11)^2+(20*12)^2+... all divided by 150 and taking the square root of this result...im getting it wrong though, does anyone see where I am mkaing my mistake.

I have some others but i think that getting and understanding these would help me figure out the others...thanks for any help and patience

 

[Andrew Mason]

Hey I am having some problems with some thermodynamics yet again. Check these out:

1) A welder using a tank of volume V fills it with oxygen (with a molar mass of M) at a gauge pressure of $$p_1$$ and temperature of $$T_1$$. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is $$T_2$$. , the gauge pressure of the oxygen in the tank is $$p_2$$.

A)Find the initial mass of oxygen.
Use R for the ideal gas constant and $$p_a$$ for atmospheric pressure.

In the ideal gas equation, what quantity are you trying to find? (hint: how is n related to mass?). Does it depend on P2 or T2? So what is the ideal gas equation you want to use? Isolate the quantity you need and work out the mass from that.

B)Find the mass of oxygen that has leaked out.

In this case, the mass of the gas lost is the difference between the original mass and the mass left in the tank. Use the ideal gas equation to find the latter the same way you did A.

2) Initially, the translational rms speed of an atom of a monatomic ideal gas is 250m/s. The pressure and volume of the gas are each doubled while the number of moles of the gas is kept constant.

What is the final translational rms speed of the atoms?

Well i was looking at the equations for RMS and all require T so how would i got about this problem?

If PV = nRT is always true, and both P and V are doubled, what must happen to T?

3) The ideas of average and root-mean-square value can be applied to any distribution. A class of 150 students had the following scores on a 100-point quiz:
Score/ Number of Students

10/ 11
20 / 12
30 / 24
40 / 15
50 / 19
60 / 10
70 / 12
80 / 20
90 / 17
100 / 10

A) a asks to find the average score of the class which i ws able to do but part b asks for the root-mean-square of the class...what i tried was something like (10*11)^2+(20*12)^2+... all divided by 150 and taking the square root of this result...im getting it wrong though, does anyone see where I am mkaing my mistake.

I have some others but i think that getting and understanding these would help me figure out the others...thanks for any help and patience

It is kind of an odd way to use RMS. But I think it would be the sum of the squares of all the test grades divided by the total number of students and then take the square root. So you would have

$$\sqrt{(10^2*11 + 20^2*12 ...100^2*10)/150}$$

AM

 

[cukitas2001]

In the ideal gas equation, what quantity are you trying to find? (hint: how is n related to mass?). Does it depend on P2 or T2? So what is the ideal gas equation you want to use? Isolate the quantity you need and work out the mass from that.

Can you elaborate some on this? n=m_tot/M where M is molar mass

I got 2 and 3 thanks for the insight

 

[Andrew Mason]

Can you elaborate some on this? n=m_tot/M where M is molar mass

I got 2 and 3 thanks for the insight

Start with PV=nRT. So n = PV/RT

For the initial case:

$$n_i = P_1V/RT_1$$

That gives you the number of moles of the gas initially, which I think you have figured out. How do you determine the mass of the gas from the number of moles? (hint: what is the molecular weight of O₂? in grams/mole?)

AM

 

[cukitas2001]

but I am not actually solving for the mass initially this is one of those symbolic answer questions because it asks to use R as the ideal gas constant and $$p_a$$ for atmospheric pressure in the answer. Its the symbolic ones that bust me where it hurts

 

[Andrew Mason]

but I am not actually solving for the mass initially this is one of those symbolic answer questions because it asks to use R as the ideal gas constant and $$p_a$$ for atmospheric pressure in the answer. Its the symbolic ones that bust me where it hurts

R is the gas constant. You don't need the atmospheric pressure to work out anything here. Just express the masses of the gas in terms of M, P1, V, and T1 or M, P2, V and T2.

AM

 

[cukitas2001]

got it ... I am going to try to do it on latex but I am still new at it so its going to take a while to get it right:

part a) $$\displaystyle{\frac{( p_1+p_a)\* V * M} {R * T_1}}$$

and part b) $$\displaystyle{\frac{V*M} {R} * ( \frac{ p_1+p_a} {T_1} - \frac { p_2+p_a} {T_2} ) }$$

This stuff is killing me though...im in for a few more hours of reading tonight...thanks for the help

 

[Andrew Mason]

got it ... I am going to try to do it on latex but I am still new at it so its going to take a while to get it right:

part a) $$\displaystyle{\frac{( p_1+p_a)\* V * M} {R * T_1}}$$

and part b) $$\displaystyle{\frac{V*M} {R} * ( \frac{ p_1+p_a} {T_1} - \frac { p_2+p_a} {T_2} ) }$$

This stuff is killing me though...im in for a few more hours of reading tonight...thanks for the help

That's right. M is in grams/mole or kg/mole. n is in moles. So mass = nM = PVM/RT

You are also right about the pa, by the way. I had overlooked that p1 and p2 are gauge pressures so the correct pressure inside the taken is p1+pa and p2+pa.

AM