Question 13.5: Suppose that a batch of parts is plated with copper in an el......
Suppose that a batch of parts is plated with copper in an electrolytic bath running at 0.15 V and 15.0 A for exactly 2 hours. What is the energy cost of this process if the electric utility charges the company $ 0.0500 per kWh?
Strategy We can determine the energy expended because we know the current, time, and voltage. The current multiplied by the time gives us the charge, which when multiplied by the voltage yields the energy. Once we know the energy expenditure we can convert the value we calculate (in J) to kWh to obtain the cost of the electricity.
Q=I \times t=15.0\text{ C s }^{-1} \times 7200\ s =1.08 \times 10^5\ C \\ \text { Energy }=\text { charge } \times \text { voltage }=1.08 \times 10^5\ C \times 0.15\ V =1.6 \times 10^4\ J
Now convert to kWh and determine the cost.
\left(1.6 \times 10^4\ J \right) \times\left(\frac{1\text{ kWh} }{3.60 \times 10^6\ J }\right) \times\left(\frac{\$ 0.0500}{1\text{ kWh} }\right)=\$ 0.00023
Analyze Your Answer This value seems small—but does it make sense? Two factors contribute to the small result: a kilowatt-hour is a rather large energy unit, and the cost per kWh is low. Thus a very small cost is not problematic. This low cost points to the importance of running electroplating at low voltage: increasing voltage would lead directly to higher cost. This example is not representative of costs in the electroplating industry, but it does help us to get a handle on some of the variables that industry must consider when implementing electrochemical techniques.
Check Your Understanding If you need 25,000 A of current to carry out electrolysis for 15 minutes, what voltage would you need if you are to use 1.7 kWh for the process?