Question

The Hoover Dam in the U.S produces 2 x 10 ^9 Watts of electricity and is composed of 7 x 10^9 kg of concrete. Concrete requires 1MJ of energy to produce 1 kg

1) How much energy did it take to produce the dam?

2) How long is the "energy payback time" for the dam?

Show your work.

Answer 1

(I). The energy is
`7*10^(9)\ MJ`.

(II). The time is
`3.5*10^(6)\ sec`.

Explanation:

Given that,

Power
`P= 2*10^(9)\ Watts = 2*10^(9)\ joule/sec`

Mass of concrete
`m= 7*10^(9)\ kg`

Concrete requires 1 MJ of energy to produce 1 kg.

(I). We need to calculate the energy

Using formula of energy

`1\ MJ =10^(6)\ J`

1 kg concrete required 10⁶ J energy.

So, The energy is

`7*10^(9)\ kg\ concrete = 7*10^(9)*10^(6)\ J`

The energy is
`7*10^(9)\ MJ`.

(II). We need to calculate the time

Using formula of power

`P=(E)/(t)`

`t=(E)/(P)`

Put the value into the formula

`t=(7*10^(9)*10^(6))/(2*10^(9)*60*60)`

`t=3500000\ sec`

`t=3.5*10^(6)\ sec`

Hence, (I). The energy is
`7*10^(9)\ MJ`.

(II). The time is
`3.5*10^(6)\ sec`.

Answer 2

1) 7 × 10⁹ MJ of energy

2) 48.611 days

Explanation:

Given:

Electricity produced by the dam = 2 × 10⁹ W

Concrete in dam = 7 × 10⁹ Kg

also,

1 MJ energy is required to produce 1 kg

or

1 × 10⁶ J is required to produce 1 kg

1) Now, the energy required for 7 × 10⁹ Kg = 7 × 10⁹ × 1 × 10⁶

or

= 7 × 10⁹ MJ of energy

2) Energy produced = 2 × 10⁹ W = 2 × 10⁹ J/s

Now,

energy payback time =
`\frac{\textup{Energy required}}{\textup{Energy produced}}`

or

energy payback time =
`(7*10^9\ MJ)/(2*10^9\ J/s)`

or

energy payback time = 3.5 × 10⁶ seconds

now,

1 day = 24 × 60 × 60 seconds = 72000 seconds

thus,

3.5 × 10⁶ seconds =
`(3.5*10^6)/(72000)` = 48.611 days