Find mass flow rate using heat differential

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SUMMARY

The discussion focuses on calculating the mass flow rate of cold water in an experimental power plant at the Natural Energy Laboratory of Hawaii, where the temperature differential between surface water (25°C) and deep water (7°C) is utilized. The cold water exits the plant at 12°C, and the key equations involved include W = QH - QC and e = 1 - TC / TH, with specific heat capacity of water set at 4190 J/kg*K. To determine the flow rate in kg/s and L/s, the relationship between temperature change (ΔT), specific heat (c), and power output (P) must be established, emphasizing the need for the plant's intended electrical power generation as a critical variable.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the specific heat capacity of water (cwater = 4190 J/kg*K).
  • Knowledge of mass flow rate calculations and related equations.
  • Basic understanding of power generation concepts in thermal systems.
NEXT STEPS
  • Research the calculation of mass flow rate using the equation dm/dt = Q / (c * ΔT).
  • Explore the relationship between power output and flow rate in thermal power plants.
  • Learn about the principles of heat exchangers and their role in energy conversion.
  • Investigate the impact of temperature differentials on efficiency in thermal systems.
USEFUL FOR

Students in engineering or physics, energy analysts, and professionals involved in thermal power generation and energy efficiency optimization will benefit from this discussion.

mckray
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Homework Statement



An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 25°C and 7°C respectively.

The cold water that enters the plant leaves it at a temperature of 12°C What must be the flow rate of cold water through the system? Give your answer in kg/s & L/s.

dm/dt = ?

Homework Equations



W = QH - QC
e = 1 - TC / TH
cwater = 4190 J/kg*K

The Attempt at a Solution



I understand that it takes a certain amount of time to raise the water from 7°C to 12°C, but I don't know how to find that or how to relate it to a flow rate.
 
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remember what you have and what you want to know. you have ΔT, c, and P (which is Q/t) and you want kg/s (which is mass/time)...i think there is an equation for that, do you remember it? remember, your answer is going to be in kg/s.
 
How much electrical power is the plant supposed to generate? That would seem to be a critical bit of information in determining how much flow is required.
 

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