You are using a gas powered pump to raise 100 kg of water to a height of 100 m. the energy efficiency of the pump is 20%. by what amount has the internal energy of the water and pump changed?

for this problem i first did:

change in potential energy = mgh
change in potential energy = 100 * 9.81 * 100
change in potential energy = 98.1 kj

but i don't know how to use the efficiency

Explanation:

An energy efficiency of 20% means that, of 100 % of energy that the pump obtains from the gas, uses 20% of that energy to perform work over the water, and losses the other 80% in the form of heat.

This means that the change in potential energy you obtained is 20% of the total internal energy that the pump has consumed:

The water is raised, changing its potential energy, but, this doesn't contributes to its internal energy. But the heat that was loosed by the pump does. Using the approximation, as good physicist, that the pump doesn't exchange heat with the surroundings, and only transfers it to the water. The water gains the heat loosed by the pump.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.