A butane fuel canister is sitting on a digital scale The can

A butane fuel canister is sitting on a digital scale. The canister is connected by a flexible hose to a burner marketed to campers / backpackers. The burner is on. Atop the burner is a thermoelectric generator / pot assembly (Powerpot V) containing boiling water. The lid is on the top of the pot, but it does not seal, so steam is emitted from the top of the pot. The thermoelectric generator output is connected to a smartphone to charge it. An in-line digital power meter registers 2.26 W delivered to the smartphone. The pot has an internal diameter of 5 inches. Experimenters had noticed that the pot was losing 3.75 inches of liquid water per hour, so they have rigged up a 1/8” diameter plastic hose to steadily feed liquid water at 20 °C from a faucet and they have adjusted the flow so the pot’s water level remains constant. Everything has been operating steadily for one hour when the experimenters record:

local pressure P = 98.84 kPa

scale reading = 421.34 g

Then, one hour later, the experimenters record:

local pressure P = 98.84 kPa

scale reading = 296.69 g

a) What is the mass flow rate of fuel into the burner [kg/s]?

Solution

Given that the whole setup is maintained on a scale to measure the weights, we knkow that the two perishable goods are water and the fuel. Since it is told that the water level that was dropping is being replenished with a constant feed, the pot\'s water level remains constant. Hence, the only change in weight must be caused by the fuel level falling.

Given initial reading = 421.34 grams

Final reading = 296.69 grams

Hence, the change in weight = 421.34 - 296.69 = 124.65 grams

Time taken for this weight to be lost = 1 hour = 3600 seconds

Hence, rate of fuel burning = 3.4625x10^-5 kg/sec