The costs of mining and transporting coal are roughly independent of the heating
ID: 107954 • Letter: T
Question
The costs of mining and transporting coal are roughly independent of the heating value of the coal. Consider that the coal in the ground is valued at 50 cents/million kJ, that mining costs are 8 dollars/ton, and that transportation costs are 8 cents/ton-mile. If the price of other delivered coals is 160 cents/million kJ, find: (a) the radius from the mine, in miles, that a coal of 32, 560 kJ/kg can be delivered and sold for zero profit or loss; (b) the same radius for a coal with a heating value of 23, 200 kJ/kg; and (c) the minimum heating value of a coal that could be used locally (i.e., a mine mouth plant).Explanation / Answer
a)The radius of mine can be found out by using the heating value,transportation cost,mining cost and value of coal in ground.
Radius of mine in miles=(transportation cost*heating value)/(value of coal*mining cost)
=(8*32,560)/((160-50)*8)
=296miles
b)Radius of mine for heating value of 23,200kJ/kg:-
Radius of mine in mile=(transportation cost*heating value)/(value of coal*mining cost)
=(8*23200)/((160-50)*8)
=210miles
c)Minimum heating value of coal that could be used locally can be found from average of calculated values of radius of mine
Average value of radius of mine=(296+210)/2=253miles
The minimum heating value=(radius of mine*value of coal*mining cost)/(transportation cost)
=(253*110*8)/(8)
=27830kJ/kg
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