Justifying the purchase of a plastic box over plastic bags.

[smalveh]

Hi, I have to calculate the amount of times a 76g polypropylene lunchbox must be used in order to justify its purchase over disposable 2g polyethylene snaplock bags, in terms of the life cycle energy of the two products. However each time the polypropylene box is used it must be washed using 500ml of hot water.

Known Data:
Energy life cycle of 2g of polyethylene = 64.2kJ (E_bag)
Energy life cycle of 76g of polypropylene = 5 578.4KJ (E_box)
Energy required to heat 500ml water from 15 °C to 45 °C = 64.6KJ (E_wash)

So now I understand the amount of times the box must be used just to make up for the energy life cycle difference between it and the bags is Uses_initial = E_box/E_bag
But where I get stuck is trying to calculate the amount of times the box must be used in order to make up for the energy lost washing the box.

This is what I've tried so far:
Uses_initial= E_box/E_bag
Uses_{due to washing} = Uses_initial * E_wash/E_bag

Now what confuses me is that every time the box must be used it must be washed, thus expending more energy, because of this loss of energy the box must be used again and then washed again, it seems to me this will go on for ever or more realistically the total uses will asymptote. How do I form a proper mathematical relationship from this.
Thanks for your help.

 

[kylebashnick]

I'm not too sure, do you think you use the calorific value and if so, how?