Question

When boiling​ water, a hot plate takes an average of 7 minutes​ [min] and 25 seconds​ [s] to boil 150 milliliters​ [mL] of water. Assume the temperature in the lab is 72 degrees Fahrenheit ​[Superscript o Baseline Upper F​]. The hot plate is rated to provide 592 watts​ [W]. If we wish to boil 150 milliliters​ [mL] 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 ​[Superscript o Baseline Upper C​]. ​[Hint: you must determine the efficiency of the​ hotplate.]

Answer 1

Given, the time taken to boil 150 ml of water is 7mins 25 secs.

The lab temperature is 72^oF = 22.22^oC. Also, we are considering the temperature of water as 22.22^oC.

Water boils at 100^oC and the specific heat of water is 4.186 joule/ gram ^oC.

Thus, total energy required to boil 150 ml of water is = (150 x 4.186 x (100 - 22.22)) = 48838.06 joules [150 ml = 150 gm]

It is mentioned that the hot plate is rated to provide 592 watts.

Thus, the energy output in 7 mins 25 secs is (592 x ((7 x 60) + 25) = 263440 joules [ 1 joule = 1 watt - sec]

Thus, the efficiency of the plate is = (48838.06/263440) x 100% = 18.54%

The specific heat of acetone is 2.15 joule/ gram ^oC. Acetone boils at 56^oC.

Thus, the energy required to boil 150 ml of acetone is = (150 x 2.15 x (56 - 22.22)) = 10894.05 joules [initial temperature is considered as 22.22 ^oC which is the lab temperature]

Since the hot plate has an efficiency of 18.54% the output energy by the hot plate per second is 18.54% of 592 = 109.75 joules

Thus, the time taken to boil the acetone is (10894.05/109.75) = 99.2 secs = 1min 39 secs (approx).

Thus, 1min 39 sec will be taken to boil 150 ml of acetone on that hot plate.