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## 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!

THANKS!

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