The expression of V(m³)=e^(t(s)) to make V in in³ and t in minutes is;
V(in³) = (¹/₆₁₀₂₄)a
We are given that;
Volume of microbial culture is observed to increase according to the formula;
V = e^(t)
where;
t is in seconds
V is in m³
We want to now express V in in³ and t in minutes.
Now, from conversions;
1 m³ = 61024 in³
Also; 1 second = 1/60 minutes
according to formula for exponential decay, we know that;
V = ae^(bt)
Thus, we have;
61024V = ae^(¹/₆₀b(t(h))
V(in³) = (¹/₆₁₀₂₄)a
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An alpha-numeric designator which is systematically assigned at the time of manufacture, so as to identify the manufacturer, month, year, location, and batch is referred to as lot number.
<h3>What is a product?</h3>
A product can be defined as any physical object (tangible item) that is typically produced by a manufacturer so as to satisfy and meet the demands, needs or wants of every customer. Also, some examples of a product include the following:
- Refrigerator
- Television
- Microwave oven
- Pencil
- Smartphone
- Computer
- Perfume
<h3>What is lot number?</h3>
A lot number can be defined as an alpha-numeric designator which is systematically designed and assigned at the time of manufacture, so as to identify the manufacturer, month, year, location, and batch.
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Answer:
a)
, b) 
Explanation:
a) The counterflow heat exchanger is presented in the attachment. Given that cold water is an uncompressible fluid, specific heat does not vary significantly with changes on temperature. Let assume that cold water has the following specific heat:

The effectiveness of the counterflow heat exchanger as a function of the capacity ratio and NTU is:

The capacity ratio is:



Heat exchangers with NTU greater than 3 have enormous heat transfer surfaces and are not justified economically. Let consider that
. The efectiveness of the heat exchanger is:


The real heat transfer rate is:




The exit temperature of the hot fluid is:




The log mean temperature difference is determined herein:



The heat transfer surface area is:



Length of a single pass counter flow heat exchanger is:



b) Given that tube wall is very thin, inner and outer heat transfer areas are similar and, consequently, the cold side heat transfer coefficient is approximately equal to the hot side heat transfer coefficient.
