An electric winch on a boat operates on 120 volts V and draw

An electric winch on a boat operates on 120 volts [V] and draws 2 amperes [A] of current. The winch has an efficiency of 35%. It is used to raise a scuba tank up 5 feet [ft] out of the water. When the tank is completely full of air, it requires 3 seconds [s] to complete this task. Assume the molecular weight of air is 29 grams per mole [g/mol]. If the tank has a mass of 14 kilograms [kg] when it is completely empty, how many moles of air are in the tank when it is completely full? Be careful to focus only on the mass of the air. Use 1 decimal place.

Solution

Solution:-

For Electric Winch,   Voltage V = 120 volts   &   Current I = 2 ampere

So, Power Input = Voltage x Current x Power Factor

(Asssuming Power Factor = 1)

Power = 120 x 2 = 240 watt

As, the efficiency of winch = 35 % = 0.35

So, Actual Power delivered by the winch = 0.35 x 240 = 84 watt

This Power will be used to lift the scuba tank filled with air.

If M = Mass of scuba tank(empty) = 14 Kg      &    m = mass of air

Height upto which tank is to be raised, h = 5 feet

Coverting in SI unit,   h = 1.524 m

Power Required to raise the scuba tank filled with air (in 3 seconds) = (M + m)gh/3

(Note - Buoyancy forces are neglected as volume of scuba tank is not mentioned in question)

So,        (M + m)gh/3 = 84

   or (M + m)gh = 3 x 84 = 252

   or      (14 + m) x 9.81 x 1.524 = 252

   or      (14 + m) = 16.8                    

   or               m = 16.8 - 14 = 2.8 kg

Molecular weight of air = 29 g/mol

So, Number of moles of air = 2.8 x 1000/29 = 96.5 mole