PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 14, Problem 113P

(a)

To determine

The temperature at the copper –steel interface.

(a)

Expert Solution
Check Mark

Answer to Problem 113P

Temperature is 103.81°C.

Explanation of Solution

Write the equation for thermal conductivity from Fourier’s law of heat conduction.

Write the relation between thermal conductivities of copper and steel.

st=Cu (I)

Here, st is the rate of heat flow of steel and Cu is the rate of heat flow of copper.

Write the equation for st.

st=κstAΔTstdst

Here, κst is the thermal conductivity of steel, A is the cross sectional area, ΔTst is the change in temperature of steel, and dst is the diameter of steel.

Write the equation for Cu.

Cu=κCuAΔTCudCu

Here, κCu is the thermal conductivity of copper, ΔTCu is the change in temperature of copper, and dCu is the diameter of copper.

Rewrite equation (I) by substituting the above relations for st and Cu.

κstAΔTstdst=κCuAΔTCudCuΔTst=κCudstκstdCuΔTCu (I)

Write the equation to find the temperature at the copper –steel interface.

ΔTst+ΔTCu=TcTb (II)

Here, Tc is the temperature of ceramic heating element and Tb is temperature of boiling water.

Write the equation for temperature at the copper –steel interface.

T=TcΔTCu (III)

Here, T is the temperature at the copper –steel interface.

Conclusion:

Substitute 401W/mK for κCu, 46.0W/mK for κst, 0.350cm for dst, and 0.150cm for dCu in equation (I).

ΔTst=(401W/mK)(0.350cm)(46.0W/mK)(0.150cm)ΔTCu=(20.3)ΔTCu

Substitute 104.00°C for Tc, 100.00°C for Tb, and (20.3)ΔTCu for ΔTst in equation (II) to find ΔTCu.

ΔTst+(20.3)ΔTCu=(104.00°C100.00°C)ΔTst=0.187°C

Substitute 104.00°C for Tc and 0.187°C for ΔTst in equation (III)

T=104.00°C0.187°C=103.81°C

Therefore, the temperature is 103.81°C.

(b)

To determine

The rate of evaporation of water from the pan.

(b)

Expert Solution
Check Mark

Answer to Problem 113P

Water evaporates at the rate of 0.565g/s.

Explanation of Solution

Write the equation for heat flow.

ΔQΔt=κstAΔTstdst

Here, ΔQ is the heat energy enters into the water and Δt is the time interval.

Write the equation for ΔQ.

ΔQ=ΔmLv

Here,Δm is the mass of water vapour and Lv is the latent heat of vaporisation of water.

Rewrite the heat flow equation by substituting the above relation for ΔQ.

ΔmLvΔt=κstAΔTstdstΔmΔt=κstAΔTstLvdst

Conclusion:

Substitute 46.0W/mK for κst, π(0.180m2)2 for A, 103.81°C100.00°C for ΔTst, 2256J/g for Lv, and 0.350cm for dcm in the above equation to find ΔmΔt.

ΔmΔt=(46.0W/mK)(π(0.180m2)2)(103.81°C100.00°C)(2256J/g)(0.350cm(102m1cm))=(5.65×104kg/s)(1g103kg)=0.565g/s

Therefore, the water evaporates at the rate of 0.565g/s.

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