Question

Suppose you stand with one foot on ceramic flooring and one on a wool carpet, making contact over a 77.2 cm2 area with each foot. Both the ceramic and the carpet are 2.60 cm thick and are 10.0°C on their bottoms. At what rate must each foot supply heat to keep the top of the ceramic and carpet at 33.0°C? The thermal conductivity of ceramic is 0.84 J/(s · m · °C) and that of wool is

Answer 1

Answer:

$P_{c$= 5.74W

$P_{w}$=0.27 W

Explanation:

d= 2.6cm =>0.026m (for both the ceramic and the carpet )

Thermal conductivity of wool '$k_{w}$'= $k_{carpet}$ = $k_{wool}$=  0.04J/(sm °C)

Thermal conducticity of carpet '$k_c}$' = 0.84 J/(sm °C)

Area 'A'= $A_{carpet}$= $A_{ceramic}$= 77.2cm²=> 77.2 x $10^{-4}$m²

$T_h}$=33.0°C

$T_c}$=10.0°C

Average Power $P_{avg}$ is determined by dividing amount of energy'Q' by time taken for the transfer't':

$P_{avg}$ = Q/Δt

Due to conductivity, heat of flow rate will be P= dQ/dt

P=$\frac{dQ}{dt}$ = $\frac{kA[T_{h}-T_{c} ]}{d}$

For CERAMIC:

$P_{c$=$\frac{k_{c} A[T_{h}-T_{c} ]}{d}$ => [0.84 x 77.2 x $10^{-4}$(33-10) ]/0.026

$P_{c$= 5.74W

For WOOL CARPET:

$P_{w}$= $\frac{k_{w} A[T_{h}-T_{c} ]}{d}$=> [0.04 x 77.2 x $10^{-4}$(33-10) ]/0.026

$P_{w}$=0.27 W