## Boiler Pump

The system in the below diagram pumps 60,000 kg of water per hour into a boiler. The pump discharges compressed liquid at 50°C and 20 MPa. The boiler discharges superheated vapor at 550°C and 20 MPa. In the boiler, what is the heat transfer rate to the working fluid?

##
__
__**Hint**

**Hint**

$$$\dot{Q}=\dot{m}(h_2-h_1)$$$

where
$$\dot{Q}$$
is the heat transfer rate on the working fluid,
$$\dot m$$
is the mass flowrate, and
$$h$$
is the specific enthalpy.

##
__
__**Hint 2**

**Hint 2**

Mass flowrate is measured in kg/sec.

An energy balance on the boiler:

$$$\dot{Q}=\dot{m}(h_2-h_1)$$$

where
$$\dot{Q}$$
is the heat transfer rate on the working fluid,
$$\dot m$$
is the mass flowrate, and
$$h$$
is the specific enthalpy.

Because mass flowrate is measured in kg/sec:

$$$\frac{60,000kg}{1hr}\cdot \frac{1hr}{60min}\cdot \frac{1min}{60sec}=\frac{60,000kg}{3,600sec}$$$

Thus,

$$$\dot Q=\frac{60,000kg}{3,600sec}\cdot [(4,000-200)\frac{kJ}{kg}]=(16.67)(3,800)\frac{kJ}{s}$$$

$$$\dot Q=63,333\:kW\approx 63\:MW$$$

63 MW