Question

You might challenge the assertion that batteries are inexpensive energy converters. Calculate the price per kWh for a 12-volt automobile battery with a 50 amp-hour capacity that sells for 40$. If its weight is 45 lb, what is the energy density in watt-hours per lb

Answer 1

Answer:

The price per kWh is $c = \ 66.67$

The energy density in watt-hours per lb is $Z = 13.33 \ Wh /lb$

Explanation:

From the question we are told that

 The voltage of the battery is  $V = 12 \ V$

 The capacity of the battery is  $I t = 50 \ amp \cdot hour$

 The  price is  $C = \ 40$

 The weight of the battery  is  $W = 45 lb$

Generally the energy generated by the battery is mathematically represented as

         $E = P * t$

Here  P is power which is represented as

        $P = I V$

So

     $E = IV * t$

=>   $E = It * V$

=>   $E =50 * 12$

=>   $E =600 \ W h$

converting to  kW h

=>   $E =\frac{600 }{1000}$      

=>   $E = 0.6 \ kWh$  

Generally the cost of this energy produced is  $C = \ 40$  Hence the cost of  1 kWh  is mathematically represented as

      $c = \frac{C}{ E}$

=>   $c = \frac{40}{ 0.6}$

=>   $c = \ 66.67$

Generally the energy density is mathematically represented as

       $Z= \frac{E}{W}$

=>    $Z = \frac{600}{45}$

=>    $Z = 13.33 \ Wh /lb$