## Exchanging of Heat

Consider a heat exchanger uses an incompressible fluid with a specific heat of 4200 J/kg∙°C to cool a closed loop system from 50°C to 25°C. If the cooling fluid flows through at 100 kg/sec, what is the rate of heat transfer in MW?

Expand Hint
The rate of heat transfer associated with either stream in a heat exchanger in which incompressible fluid or ideal gas with constant specific heats flows:
$$\dot{Q}=\dot{m}c_{p}(\Delta T)$$$where $$\dot{m}$$ is the mass flow rate, $$c_p$$ is the specific heat at constant pressure, and $$\Delta T$$ is the change in temperature. Hint 2 There is no need to convert the temperatures to Kelvin since they will cancel out. The rate of heat transfer associated with either stream in a heat exchanger in which incompressible fluid or ideal gas with constant specific heats flows: $$\dot{Q}=\dot{m}c_{p}(\Delta T)$$$
where $$\dot{m}$$ is the mass flow rate, $$c_p$$ is the specific heat at constant pressure, and $$\Delta T$$ is the change in temperature.
$$\dot{Q}=(100\frac{kg}{s})(4,200\frac{J}{kg\cdot ^{\circ}C})(50^{\circ}C-25^{\circ}C)$$$$$\dot{Q}=(\frac{100}{s})(4,200J)(25)=10,500,000\:\frac{J}{s}$$$
$$\dot{Q}=10.5\:MW$$\$
10.5 MW
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