Please tell me where i went wrong.

During an all-night cram session, a student heats up a one-half liter (0.50 10-3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 19°C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 90°C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?

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Physics - bobpursley, Friday, April 13, 2007 at 10:08am
Wouldn't you use the volume coefficent of water, and compute the new volume? I will be happy to critique your work.

delta V = (coeffiecient of volume expansion of water)(volume of coffee)(change in temp)

delta V = (207e-6)(0.5e-3m^3)(90deg C-19 deg C)

delta V = 0.000007349 m^3

delta V = (0.5e-3) - 0.000007349

delta V = 0.000492651

delta V = 0.000007349 m^3. That is how much the coffee expands. That is , lets see, 7.3 cc. I think that is what the problem is asking.

Well, it seems like your calculations are correct, but you made a small mistake when writing down the final answer. The correct answer is 0.000007349 m^3, which is approximately 7.3 milliliters, not 7.3 cubic centimeters. So, the coffee that spilled out of the beaker is about the size of a small shot glass. I hope that puts your mind at ease!

To find the amount of coffee that has spilled out of the beaker, you need to calculate the change in volume of the coffee due to the temperature increase.

1. Begin by calculating the change in volume (delta V) using the formula: delta V = (coefficient of volume expansion of water) x (volume of coffee) x (change in temperature)

Given:
- Coefficient of volume expansion of water = 207e-6 (per degree Celsius)
- Volume of coffee = 0.50 x 10^-3 m^3
- Change in temperature = 90°C - 19°C = 71°C

2. Calculate delta V:
delta V = (207e-6) x (0.50e-3) x (71)
= (0.000207) x (0.00050) x (71)
= 0.000007349 m^3

The change in volume of the coffee is 0.000007349 m^3.

3. To find the spilled volume, subtract the change in volume from the initial volume:
Spilled volume = (initial volume) - (delta V)
= (0.50 x 10^-3 m^3) - (0.000007349 m^3)
= 0.000492651 m^3

Approximately, 0.000492651 m^3 or 7.3 cubic centimeters (cc) of coffee has spilled out of the beaker.

To solve this problem, you need to use the formula for calculating the change in volume due to thermal expansion:

ΔV = (coefficient of volume expansion) * (initial volume) * (change in temperature)

In this case, the coefficient of volume expansion for water can be used since the coefficient for coffee is the same.

Given:
Initial temperature (T1) = 19°C
Final temperature (T2) = 90°C
Initial volume (V) = 0.50 * 10^-3 m³

First, calculate the change in temperature:
ΔT = T2 - T1 = 90°C - 19°C = 71°C

Next, find the coefficient of volume expansion for water. From reference tables, it is approximately 207 × 10^-6 /°C.

Now, plug the values into the formula:

ΔV = (207 × 10^-6 /°C) * (0.50 * 10^-3 m³) * (71°C)

Calculate:
ΔV ≈ 0.007349 m³

So, the change in volume of the coffee is approximately 0.007349 cubic meters.

To find how much coffee has spilled out of the beaker, subtract the change in volume from the initial volume:

Spilled volume = Initial volume - Change in volume
= 0.50 * 10^-3 m³ - 0.007349 m³
≈ 0.492651 * 10^-3 m³

Therefore, approximately 0.492651 cubic millimeters (cc) of coffee has spilled out of the beaker.

Use the density of water as 210*10^-6

so

(210*10^-6)(0.5*10^-3)(90-19)
= 7.455*10^-6
or 0.000007455