THERMODYNAMICS  CASE STUDY



Introduction 
Iron and Iron Board 

Before ironing, an iron needs to be
warmed up to a certain temperature. The iron temperature is different
for different fabric. The resistance wires are used to generate the energy
needed to warm the iron up.
Known:

The power of the iron is =
100 W and 85% of the heat generated in the resistance wires is
transferred to the iron base plate
 The materials of the base plate is aluminum alloy
202476 (ρ = 2770 kg/m^{3} and
c_{p}=
875 J/(kg^{o}C)) and the base plate thickness δ =
0.5 cm, and the area is A = 0.02 m^{2}
 Initially the iron is in equilibrium with the ambient air at
T_{initial} = 20^{o}C
 The convection heat transfer coefficient h = 35 W/(m^{2}^{o}C)
 The emissivity of the base plate to the ambient ε = 0.6






Questions 



Determine the minimum time needed for the base plate
temperature to reach T_{final} = 140^{o} C.

After the temperature reaches
140^{o} C,
how much energy is needed to keep the base at 140^{o} C?






Approach 
Energy Balance Diagram 


The heat needed to increase the base plate's temperature
from T_{inital} to T_{final} is:
Q = c_{p} m (T_{final}  T_{initial})
where
m = mass of the base
c_{p} = specific heat

The energy balance of the base plate (Energy balance
will be introduced in the following section):
 Energy in: 85% of the heat generated by the wires.
 Energy out: convection, radiation heat loss to the ambient air.
 Energy storage: the energy in the base to increase the base's temperature.
E_{in}  E_{out} = E_{storage}



