Question

When the capacity of a hydrogen plant is doubled, the capital cost increases by 73%.
1.1. Why does the capital cost not double when the capacity is doubled? (2)
1.2. Derive an equation that relates the capacity to the capital cost for this particular hydrogen
plant. (6)
1.3. If the six-tenth rule is used, what would be the increase in the capital cost if the hydrogen
plant capacity is doubled? Compare this increase with the 73% mentioned above and
comment. (5)

Answer 1

The capital cost did not double when the capacity of the plant is doubled. This phenomenon is due to technical economies. Large plants have more efficiency. The capita cost of a plant does not increase in proportion to the size of the plant. This is because the main cost of infrastructure and machinery does not double when the capacity gets doubled. The increase in size may double the expected output and this results in fall of the average cost. This phenomenon is also referred to as the principle of increased dimensions.

1. 

3. Using six-tenth rule,

            n= 0.6

            C_a=KAⁿ

            C_b=K(2A)ⁿ

C_b/C_a= (2A/A)^0.6 = 2^0.6 = 1.52

So, the percentage increase = (1.52-1/1)*100 = 52%

As per the six-tenths rule, larger the capacity, lower is the capacity cost. This pertains to the economies of scale.