During an all-night cram session, a student heats up a 0.360 liter (0.360 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18.1 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 94.6 °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?
dV = V0 â (t1 - t0)
therefore
0.00036*0.000214(of water?)(94.6-18.1)
=
dV = V1 - V0 = change in volume
= answer
is this correct or am I way off
Your equation looks correct, but you need to use the coefficient of volume expansion of Pyrex glass, not water. The equation you provided is for the change in volume of a substance due to temperature change.
The coefficient of volume expansion of Pyrex glass is about 9 x 10^-6 per degree Celsius. Using this information, you can calculate the change in volume of the glass beaker as:
ΔV = V0 * β * (t1 - t0)
Where:
ΔV is the change in volume
V0 is the initial volume of the beaker (0.360 L = 0.360 x 10^-3 m^3)
β is the coefficient of volume expansion of Pyrex glass (9 x 10^-6 / °C)
t1 is the final temperature (94.6°C)
t0 is the initial temperature (18.1°C)
Now you can substitute the values into the equation:
ΔV = (0.360 x 10^-3 m^3) * (9 x 10^-6 / °C) * (94.6°C - 18.1°C)
Simplifying and calculating the expression will give you the amount of volume that has spilled out of the beaker.
Your approach is mostly correct, but there are a few minor errors in your calculations. Let's break it down step by step.
First, we need to calculate the change in volume of the coffee using the formula:
dV = V0 * β * (t1 - t0)
where:
- dV is the change in volume
- V0 is the initial volume of the coffee (0.360 x 10^(-3) m^3)
- β is the coefficient of volume expansion of water (assumed to be the same as that of coffee)
- t1 is the final temperature (94.6 °C)
- t0 is the initial temperature (18.1 °C)
Now, let's plug in the values:
dV = 0.360 x 10^(-3) m^3 * β * (94.6 °C - 18.1 °C)
The coefficient of volume expansion of water (and coffee in this case) is β = 0.000214 °C^(-1), so we substitute the value:
dV = 0.360 x 10^(-3) m^3 * 0.000214 °C^(-1) * (94.6 °C - 18.1 °C)
Simplifying further:
dV = 0.360 x 10^(-3) m^3 * 0.000214 °C^(-1) * 76.5 °C
Now, let's calculate the final result:
dV = 0.360 x 10^(-3) m^3 * 0.000214 °C^(-1) * 76.5 °C
= 0.0000059654 m^3
Therefore, approximately 0.0000059654 cubic meters of coffee has spilled out of the beaker during the temperature change.
Remember to take care of unit conversions and be aware of the coefficient of volume expansion being in °C^(-1).