A frying pan is quickly heated on the stovetop 200CIt has an iron handle that is 20cmlong. Estimate how much time should pass before the end of the handle is too hot to grab with your bare hand. (Hint: The cross-sectional area of the handle doesn't matter. The density of iron is about7.9g/cm3and its specific heat is 0.45J/gC).

Short Answer

Expert verified

From the following the time taken for the handle to heat is 8.25minutes

Step by step solution

01

Introduction

Assume we have a hot frying pan of 200Con a stove. Assuming that the iron handle is in good condition (length 20cm) the pan starts at room temperature 20C, The given density of iron is 7.9×103kgm3, its specific heat capacity is c=450Jkg1K1and the thermal conductivity of iron is kt=80Js1K1, The rate of heat flow is:

QΔt=ktAΔTΔx

where Ais the cross-sectional area of the handle

Taking ΔT=20020=180Kand Δx=0.2m, We can assume that all of the heat that passes along the handle is used to heat the iron (which isn't entirely true, because some of the heat will evaporate into the surrounding air, but we can ignore this because air's thermal conductivity is relatively low compared to iron's).

02

Time taken by the handle to heat completely

The rate at which heat enters the handle is then measured.:

let it equation (1),

QΔt=80A1800.2=7.2×104A

(Assuming a cylindrical handle), the mass of iron that is being heated is:

m=ρV=ρhA=7.9×103×0.2A

m=1580Akglet be equation (2)

In time Δt, therefore, the temperature will increase by (using equation (1)):

ΔT=[Q]mc=7.2×104AΔtmc

substitute from equation (2) and with c=450Jkg1K1, so:

ΔT=7.2×104AΔt1580A×450=0.101Δtlet be equation(3)

A temperature of around Tf=70Cis probably hot, so we're looking for:

ΔT=TfTi

Where, Ti=20so:

ΔT=7020=50K

So, from equation (3),

ΔT=0.101ΔtΔt=10.101ΔT=10.101×50

T=495s=8.25min

So it would take around 8.25minutes for the handle to heat that much.

The mass of iron that is being heated (assuming a cylindrical handle) is: 70, therefore it would take around 8.25minutes for the handle to heat that much.

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