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

Answer:

1) 7 × 10⁹ MJ of energy

2) 48.611 days

Step-by-step 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 = $\frac{7\times10^9\ MJ}{2\times10^9\ J/s}$

or

energy payback time = 3.5 × 10⁶ seconds

now,

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

thus,

3.5 × 10⁶ seconds = $\frac{3.5\times10^6}{72000}$ = 48.611 days

Answer 2

Answer:

(I). The energy is $7\times10^{9}\ MJ$.

(II). The time is $3.5\times10^{6}\ sec$.

Step-by-step explanation:

Given that,

Power $P= 2\times10^{9}\ Watts = 2\times10^{9}\ joule/sec$

Mass of concrete $m= 7\times10^{9}\ kg$

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

$7\times10^{9}\ kg\ concrete = 7\times10^{9}\times10^{6}\ J$

The energy is $7\times10^{9}\ MJ$.

(II). We need to calculate the time

Using formula of power

$P=\dfrac{E}{t}$

$t=\dfrac{E}{P}$

Put the value into the formula

$t=\dfrac{7\times10^{9}\times10^{6}}{2\times10^{9}\times60\times60}$

$t=3500000\ sec$

$t=3.5\times10^{6}\ sec$

Hence, (I). The energy is $7\times10^{9}\ MJ$.

(II). The time is $3.5\times10^{6}\ sec$.