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

The price per kWh is
`c = \$ 66.67`

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

Step-by-step 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 =(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 = (C)/( E)`

=>
`c = (40)/( 0.6)`

=>
`c = \$ 66.67`

Generally the energy density is mathematically represented as

`Z= (E)/(W)`

=>
`Z = (600)/(45)`

=>
`Z = 13.33 \ Wh /lb`