Question

When boiling water, a hot plate takes an average of 8 minutes and 55 seconds to boil 100 milliliters of water. Assume the temperature in the lab is 75 degrees Fahrenheit. The hot plate is rated to provide 283 watts. If we wish to boil 100 milliliters of acetone using this same hot plate, how long do we expect the process to take? Acetone has a boiling point of 56 degrees Celsius. The specific heat capacity of water is 4.18 joules per gram degree Celsius. Acetone has a specific gravity of 0.785 and a specific heat capacity of 2.15 joules per gram degree Celcius. [Hint: You must determine the efficiency of the hotplate.]

Answer 1

Answer:

90.9 seconds

Explanation:

m = Mass of liquid = Volume×Density

c = Specific heat

$\Delta T$ = Change in temperature

t = Time taken

Room temperature = 75 °F

Converting to Celsius

$(75-32)\times \frac{5}{9}=23.889\ ^{\circ}C$

Heat required to raise the temperature of water

$Q=mc\Delta T\\\Rightarrow Q=100\times 10^{-6}\times 1000\times 4186\times (100-23.889)\\\Rightarrow Q=31860.0646\ J$

Power

$P=\frac{Q}{t}\\\Rightarrow P=\frac{31860.0646}{8\times 60+55}\\\Rightarrow P=59.55152\ W$

Efficiency of the plate

$\frac{59.5512}{283}\times 100=21.04282\%$

Heat required to raise the temperature of water

$Q=mc\Delta T\\\Rightarrow Q=100\times 10^{-6}\times 784\times 2150\times (56-23.889)\\\Rightarrow Q=5412.63016\ J$

$P=\frac{Q}{t}\\\Rightarrow t=\frac{Q}{P}\\\Rightarrow t=\frac{5412.63016}{0.2104282\times 283}\\\Rightarrow t=90.9\ s$

Time taken to heat the aceton is 90.9 seconds