Q: A fermentation broth is being cooled in a heat exchanger. The specific heat capacity ($$c_p) of $$the broth is $$2.30\ \mathrm{kJ\ kg$$^{-1}$$\ K$$^{-1}$$}. If $$the temperature drops from $$371.9\ \mathrm{K} to$$ $$349.7\ \mathrm{K}$$, what is the change in enthalpy per kilogram of broth?

$$\Delta h = c_p \Delta T = 2.30 \times (349.7 - 371.9) = -51.06\ \mathrm{kJ\ kg$$^{-1}$$}$$

Q: A nutrient medium is cooled from $$90^\circ\mathrm{C} to$$ $$25^\circ\mathrm{C} at a $$flow rate of $$2800\ \mathrm{g\ s$$^{-1}$$}. $$The specific heat capacity is $$4.187\ \mathrm{kJ\ kg$$^{-1}$$\ K$$^{-1}$$}. $$What is the rate of heat removal required (in kW)?

$$Q = m \times c_p \times \Delta T = 2.8 \times 4.187 \times (25 - 90) = -763.7\ \mathrm{kW}$$

Q: A cooling water stream enters a heat exchanger at $$15^\circ\mathrm{C}$$ with a volumetric flow rate of $$36\ \mathrm{m^3$\ h$$^{-1}$$}$$ and density $$1000\ \mathrm{kg\ m$$^{-3}$$}. $$What is the mass flow rate of the water in $$\mathrm{kg\ s$$^{-1}$$}$$?

$$m = 36 \times 1000 / 3600 = 10\ \mathrm{kg\ s$$^{-1}$$}$$

Question 1

Which of the following best explains why energy balances are critical in large-scale bioprocesses?

Accepted Answer

Because biological catalysts are highly sensitive to temperature changes, and uncontrolled heat release can cause cell death or enzyme denaturation.

Question 2

Which of the following equations correctly represents the definition of enthalpy for a thermodynamic system?

Accepted Answer

$$H = U + pV$$

Question 3

A fermentation broth is being cooled in a heat exchanger. The specific heat capacity ($$c_p) of $$the broth is $$2.30\ \mathrm{kJ\ kg$$^{-1}$$\ K$$^{-1}$$}. If $$the temperature drops from $$371.9\ \mathrm{K} to$$ $$349.7\ \mathrm{K}$$, what is the change in enthalpy per kilogram of broth?

Accepted Answer

$$\Delta h = c_p \Delta T = 2.30 	imes (349.7 - 371.9) = -51.06\ \mathrm{kJ\ kg$$^{-1}$$}$$

Question 4

Which of the following statements about enthalpy is TRUE?

Accepted Answer

Enthalpy is a state function, meaning its value depends only on the state of the system and not on the path taken.

Question 5

In a steady-state double-pipe heat exchanger with no shaft work and no phase change, which of the following is the correct energy balance for the hot and cold fluids?

Accepted Answer

$$m_h c_{p,h} (T_{h,in} - T_{h,out}) = m_c c_{p,c} (T_{c,out} - T_{c,in})$$

Question 6

A nutrient medium is cooled from $$90^\circ\mathrm{C} to$$ $$25^\circ\mathrm{C} at a $$flow rate of $$2800\ \mathrm{g\ s$$^{-1}$$}. $$The specific heat capacity is $$4.187\ \mathrm{kJ\ kg$$^{-1}$$\ K$$^{-1}$$}. $$What is the rate of heat removal required (in kW)?

Accepted Answer

$$Q = m 	imes c_p 	imes \Delta T = 2.8 	imes 4.187 	imes (25 - 90) = -763.7\ \mathrm{kW}$$

Question 7

Which of the following best describes 'flow work' in the context of energy balances for flow systems?

Accepted Answer

The energy required to push matter into or out of the system, given by $$W_f = pV$$

Question 8

A cooling water stream enters a heat exchanger at $$15^\circ\mathrm{C}$$ with a volumetric flow rate of $$36\ \mathrm{m^3$\ h$$^{-1}$$}$$ and density $$1000\ \mathrm{kg\ m$$^{-3}$$}. $$What is the mass flow rate of the water in $$\mathrm{kg\ s$$^{-1}$$}$$?

Accepted Answer

$$m = 36 	imes 1000 / 3600 = 10\ \mathrm{kg\ s$$^{-1}$$}$$

Question 9

Which of the following is the correct SI unit for energy?

Accepted Answer

$$\mathrm{kg\ m^2$\ s$$^{-2}$$} ($$joule)

Question 10

In a heat exchanger, if the hot fluid undergoes no phase change, which property is primarily responsible for the enthalpy change?

Accepted Answer

The temperature change of the fluid (sensible heat)

Question 11

Which of the following best describes the difference between heat and work in energy transfer?

Accepted Answer

Heat is energy transferred due to a temperature difference, while work is energy transferred by any other driving force.

Question 12

A process requires raising the temperature of $$1\ \mathrm{kg} of $$water by $$1^\circ\mathrm{C} at$$ $$1\ \mathrm{atm}. $$How much energy is required in joules, using the thermochemical calorie?

Accepted Answer

$$1\ \mathrm{cal} = 4.184\ \mathrm{J}$$, so energy required is $$4.184\ \mathrm{J}$$

Question 13

Which of the following is NOT an assumption made when applying the energy balance to a double-pipe heat exchanger under steady-state conditions?

Accepted Answer

There is a significant phase change in the fluids.

Question 14

A heat exchanger is used to cool a fermentation medium from $$98.7^\circ\mathrm{C} to$$ $$75.5^\circ\mathrm{C} at a $$flow rate of $$3630\ \mathrm{kg\ h$$^{-1}$$}. $$The specific heat capacity is $$2.30\ \mathrm{kJ\ kg$$^{-1}$$\ K$$^{-1}$$}. $$What is the total heat removed per hour (in kJ)?

Accepted Answer

$$Q = 3630 	imes 2.30 	imes (75.5 - 98.7) = -193,239\ \mathrm{kJ\ h$$^{-1}$$}$$

Question 15

Which of the following best describes why enthalpy cannot be measured in absolute terms?

Accepted Answer

Because internal energy cannot be measured absolutely, only changes in enthalpy can be determined.

Question 16

A heat exchanger operates at steady state with no shaft work. If the hot fluid enters at $$120^\circ\mathrm{C}$$ and leaves at $$80^\circ\mathrm{C}$$, and the cold fluid enters at $$30^\circ\mathrm{C}$$, what is the maximum possible exit temperature of the cold fluid (assuming equal mass flow rates and specific heats)?

Accepted Answer

$$80^\circ\mathrm{C}$$

Question 17

Which of the following is a real-world consequence of failing to remove heat efficiently in a large-scale bioprocess?

Accepted Answer

Cell death or enzyme denaturation due to overheating.

Question 18

Which of the following best describes the log-mean temperature difference (LMTD) in heat exchanger calculations?

Accepted Answer

It is a weighted average temperature difference used to calculate heat transfer when the temperature difference varies along the length of the exchanger.

Energy Balances and Heat Exchangers: Principles and Calculations

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