What is the final volume of the container?

In summary, the problem involves finding the final volume of a container filled with a monatomic gas after 15 seconds with a heater of 25 W power turned on. Using the formulas pV = nRT and Q = p_{power}\Deltat = nC_{p}\DeltaT, and knowing the initial volume, pressure, and temperature, the final volume can be found by first solving for the final temperature and then plugging in all known values. However, a mistake was made in the calculation involving the gas constant R, which resulted in an incorrect final volume. Further corrections need to be made to obtain the correct final volume.
  • #1

Homework Statement

A container has a 100 cm^2 piston with a mass of 10 kg that can slide up and down vertically without friction and is placed below a heater.
Suppose the heater has 25 W of power and are turned on for 15 s. What is the final volume of the container?

Initial Volume: 800 cm[tex]^{3}[/tex]
Initial Pressure: 1.11*10[tex]^{5}[/tex] Pa
Initial Temperature: 20 C

Homework Equations

pV = nRT
Q = p_{power}[tex]\Delta[/tex]t = nC_{p}[tex]\Delta[/tex]T

The Attempt at a Solution

Using pV = nRT and knowing that p_i = p_f I can get V_{f} = V_{i}T_{f} / T_{i}

I now need T_{f}

To get that I used
p_{power}[tex]\Delta[/tex]t = nC_{p}[tex]\Delta[/tex]T

to get

T_{f}] = p_{power}[tex]\Delta[/tex]t/nC_{p}] + T]_{i}

Then I used p_{i}V_{i} = nRT_{i} to replace n and I got (after much simplifying)

V_{f} = p_{power}*[tex]\Delta[/tex]t*R/[ p_{i}C_{p} ] + 1

I then plugged in all the numbers (using C_{p} of water = 4100 and got:

25*15*8.314/(1.11*10^5*4100) + 1 = 1.00000685 m^3

Which gives [tex]\approx[/tex] 1.000006.85 * 10^6 cm^3

I have a very hard time believing that is the answer -- it's just too large.

Any help pointing out the stupid thing(s) I did would be very appreciated!

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  • #2
Hi houseguest,

Did you type in the entire question? You used C_p of water in part of your solution, but I don't see where water appears in the problem.
  • #3
Sorry, I forgot to mention that the container is filled with water.
  • #4
I hope I'm not misunderstanding the problem. However one point is that if the container volume is increasing because it's filled with water and the water volume is increasing, then you cannot use PV=nRT. (That applies to ideal gases.) Instead use the formula for volume expansion of a solid or liquid.
  • #5
Wow! I'm sorry, that was definitely one of my stupid things. Thanks for pointing that out! The container is filled with a monatomic gas. So I should be using C_p for that.
So, since C_p = R + C_v and C_v = 3/2 * R ( for a monatomic gas) then C_p = 5/2 * R

So that would give ( with the R's canceling)

25*15/(1.11*10^5 * 5/2) + 1 = 1.00135 m^3 = 1.00135 * 10^6 cm^3

However, this (I would think) is still too large. Any ideas?

Thanks for your help!
  • #6
I see at least one error involving R. Try carrying your units along with each term to make sure everything cancels out OK.

1. What is the definition of final volume in a container?

The final volume of a container is the total amount of space inside the container that is occupied by a substance or mixture at the end of an experiment or process.

2. How is the final volume of a container measured?

The final volume of a container is typically measured in units of volume such as liters (L) or milliliters (mL) using tools like graduated cylinders or measuring cups.

3. Does the final volume of a container change over time?

The final volume of a container can change over time depending on factors such as temperature, pressure, and the addition or removal of substances from the container.

4. Why is knowing the final volume of a container important in scientific experiments?

The final volume of a container is important in scientific experiments because it allows scientists to accurately measure and calculate the amount of a substance or mixture present, which is essential for understanding the results of an experiment and drawing conclusions.

5. How does the final volume of a container relate to other measurements such as mass and density?

The final volume of a container is closely related to other measurements such as mass and density. For example, knowing the final volume and mass of a substance can help calculate its density, which is a measure of how much matter is packed into a given volume.

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