Question

The constant factor for converting tex count to cotton count is

• A. 100
• B. 590.5
• C. 5315
• D. 1.1

Hint:

• Tex (Direct system) Mass in grams per 1000 meters. (Higher Tex = Coarser yarn).
• Cotton Count (NeC) (Indirect system) Number of 840-yard hanks per pound. (Higher NeC = Finer yarn).
• The conversion formula is Tex $\times$ NeC = Constant.

Answer 1

The Correct Option is B

Understanding Yarn Count Systems:

1. Tex (Direct System):
   - Weight per unit length.
   - Definition: Mass in grams of 1000 meters of yarn.
   - Formula:
    

\[ \text{Tex} = \frac{\text{Weight (g)}}{\text{Length (m)}} \times 1000 \]

1. Cotton Count (Ne, Indirect System):
   - Length per unit weight.
   - Definition: Number of 840-yard hanks per pound.
   - Formula:
    

\[ \text{Ne} = \frac{\text{Length (yards)}}{\text{Weight (lbs)}} \times \frac{1}{840} \]

Conversion Between Tex and Cotton Count:

Since Tex and Ne are inversely related, the conversion requires a constant factor based on unit conversions.

Derivation of the Conversion Factor:

1. Convert Tex to grams per meter:
    

\[ 1 \text{ Tex} = 1 \text{ g per 1000 meters} = 0.001 \text{ g/m} \]

1. Convert grams to pounds and meters to yards:
   - \( 1 \text{ lb} = 453.592 \text{ g} \)
   - \( 1 \text{ yard} = 0.9144 \text{ m} \)
   - \( 840 \text{ yards} = 768.1 \text{ m} \)
2. Relate Tex to Cotton Count (Ne):
    

\[ \text{Ne} = \frac{\text{Length (yards)}}{\text{Weight (lbs)}} \times \frac{1}{840} \]

1. Substitute weight in terms of Tex:
    

\[ \text{Weight (lbs)} = \frac{\text{Tex} \times \text{Length (m)}}{1000 \times 453.592} \]

1. For \( 1 \text{ hank} = 840 \text{ yards} = 768.1 \text{ m} \):
    

\[ \text{Ne} = \frac{768.1}{\left( \frac{\text{Tex} \times 768.1}{1000 \times 453.592} \right)} \times \frac{1}{840} \]

1. Simplifying:

\[ \text{Ne} = \frac{1000 \times 453.592}{\text{Tex} \times 840} = \frac{453592}{\text{Tex} \times 840} = \frac{590.5}{\text{Tex}} \]

Final Conversion Formula:

\[ \boxed{\text{Ne} = \frac{590.5}{\text{Tex}}} \] 

Why Other Options Are Incorrect?

Option	Value	Validity
100	Incorrect	Too small; does not account for unit conversions.
590.5	Correct	Derived from exact unit conversions (lb → g, m → yd).
5315	Incorrect	Too large; likely a miscalculation.
1.1	Incorrect	Arbitrary; no mathematical basis.

Conclusion:

The correct constant factor for converting Tex to Cotton Count (Ne) is 590.5.

Final Answer: 590.5 is the constant factor.