Thermodynamic Homework Problem Check

In summary: By using the correct molar masses for helium and argon, we can see that their average speeds are actually different. This is because the average speed is affected by the mass of the molecule. So, while the average speed of a helium atom and an argon atom may be the same, the rms speed (which takes into account the mass of the molecule) will be different. Therefore, statement (b) is false. In summary, the average speed of helium and argon atoms is the same, but the rms speed is different due to the difference in their molar masses.
  • #1
fallen186
41
0
Can you check over my answers to see if my reasoning is correct?

Homework Statement


#3) "Yesterday I woke up and it was 20°F in my bedroom," said Mert to his old friend Mort. "That's nothing," replied Mort. "My room was -5.0°C." Who had the colder room, Mert or Mort?


Homework Equations


[tex]t_{F} = \frac{9}{5}*t_{c} + 32°F[/tex]


The Attempt at a Solution


Mort's -5.0°C Room conversion:
[tex]t_{F} = \frac{9}{5}*t_{c} + 32°F[/tex]

[tex]t_{F} = \frac{9}{5}*(-5.0C) + 32°F[/tex]

[tex]t_{F} = -9C + 32°F[/tex]

[tex]t_{F} = 23°F[/tex]

Mort = 23°F
Mert = 20°F

Mert has the colder room.

Homework Statement


#7) If a vessel contains equal amounts, by mass, of helium and argon, which of the following are true?
(a) The partial pressure exerted by each of the two gases on the walls of the container is the same
(b) The average speed of a helium atom is the same as that of an argon atom.
(c) The number of helium atoms and argon atoms in the vessel are equal.
(d) None of the above.


Homework Equations


(a) PV=nRT


The Attempt at a Solution


(a) False PV = nRT since V, R, and T are the same then what really matters is the relationship between P and n. If n is greater than P increases as well (direct relationship). Since both gases are the same by mass that means there is more moles of helium due to its small molar mass. Helium thus has more partial pressure than argon.
(b) True The equation [tex] v_{rms} = \sqrt_{\frac{3kT}{m}}[/tex]. Since helium and argon have the same mass their speeds are the same.
(c) False . since they're are equal by mass and have different molar masses they have different amount of moles and different amount of atoms.
(d) False. It's false because b is true

Question about the rms speed of molecules.

Book explanation:
The rms speed of a molecule of a gas is related to the absolute temperature by [tex] v_{rms} = \sqrt_{(v^{2})_{av}} = \sqrt_{\frac{3kT}{m}} = \sqrt_{\frac{3RT}{M}} [/tex] where m is the mass of the molecule and M is the molar mass.

For part b of the previous question. If i used
[tex] \sqrt_{\frac{3kT}{m}}[/tex] then I get the same speed but if i use

[tex]\sqrt_{\frac{3RT}{M}} [/tex] then i get a different speed.

Can someone help me explain this?
 
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  • #2
Surely both m and M are different for Helium and Argon.
Helium has a molar mass of 4 g/mol and a molecular mass of 4*1.67*10^-27 kg.
Argon has a molar mass of 40 g/mol and a molecular mass of 40*1.67*10^-27 kg
 
  • #3
Delphi51 said:
Surely both m and M are different for Helium and Argon.
Helium has a molar mass of 4 g/mol and a molecular mass of 4*1.67*10^-27 kg.
Argon has a molar mass of 40 g/mol and a molecular mass of 40*1.67*10^-27 kg

Thanks. This helps a lot.
 

1. What are the main concepts of thermodynamics?

The main concepts of thermodynamics include energy, heat, and entropy. Thermodynamics is a branch of physics that deals with the study of how energy is transferred and transformed between different forms.

2. How do you solve a thermodynamics homework problem?

To solve a thermodynamics homework problem, you need to first identify the given information and what is being asked. Then, use the laws and principles of thermodynamics to set up equations and solve for the unknowns. It is important to use proper units and pay attention to the signs of the variables.

3. Can you provide an example of a thermodynamics homework problem?

Sure! An example of a thermodynamics homework problem could be: "A gas is compressed from 3 L to 2 L at a constant pressure of 2 atm. If the initial temperature is 300 K, what is the final temperature of the gas?"

4. How do you check if your answer to a thermodynamics homework problem is correct?

To check if your answer to a thermodynamics homework problem is correct, you can use the laws and principles of thermodynamics to see if your answer satisfies them. You can also plug your answer back into the original problem and see if it gives the correct result.

5. Are there any common mistakes to avoid when solving thermodynamics homework problems?

Yes, some common mistakes to avoid when solving thermodynamics homework problems include using incorrect units, not paying attention to the signs of the variables, and not properly applying the laws and principles of thermodynamics. It is also important to double-check your calculations to avoid computational errors.

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