EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
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Chapter 20, Problem 37P

(a)

To determine

To Calculate:The thermal current in each cube.

(a)

Expert Solution
Check Mark

Answer to Problem 37P

The thermal current in copper cube is approximately 0.96 kW .

The thermal current in aluminum cube is approximately 0.57 kW .

Explanation of Solution

Given:

Thermal conductivity of copper, KCu=401W/mK

Areaof cross-section of copper, Acu=9.0×104

Temperature difference, ΔT=80K

Thermal conductivity of aluminum, KAl=237W/mK

Areaof cross-section of aluminum, AAl=9.0×104

Formula used: The amount of heat (ΔQ) conducted per unit time (Δt) is

  ΔQΔt=kΑΔΤL ..........(1) 

Here, L the thickness of the substance. The cross-section area of the substance, ΔT the

temperature difference among the ends of the substance and k the thermal conductivity of thesubstance.

The thermal resistance is given by:

  R=LkA

Then the equation (1) is written as

  ΔQΔt=ΔΤR 

Here, the thermal current I=ΔΤR 

Calculation:

The thermal current within each cube, is expressed as follows:

  I=ΔΤkAΔx

The thermal resistance of each cube is:

  R=ΔxkA

By using the equation (2), the thermal current through the copper can be expressed as follows:

  I=ΔΤKCuACuΔxCu

  ICu=( 401W/m·K) ( 9×10 -4 m 2 )( 80K) 3×10 -2 m= 962 W( 1kW 1000W)= 0.962 kW

By using the equation (2), the thermal current through the Aluminum can be expressed asfollows:

  I=ΔΤKAlAAlΔxAl

  IAl=( 237 W/m·K)( 9×10 -4 )( 80K) 3×10 -2 m= 568.8 W( 1 kW 1000 W)= 0.57 kW

Hence, the thermal current in aluminum cube is approximately 0.57 kW .

Conclusion: The thermal current in each cube is to be calculated by using temperature difference and thermal conductivity.

(b)

To determine

To Calculate: The total thermal current.

(b)

Expert Solution
Check Mark

Answer to Problem 37P

The total thermal current is 1.53kW

Explanation of Solution

Given:Current passing through the copper (Icu) is 962 W .

Current passing through the aluminum (IAl) is 568.8 W .

Formula used:

Given that the cubes are in parallel, therefore total thermal current can be expressed as:

  I = 1Cu +IAI

Calculation:

Substitute the values and solve:

  I = 962 W +569W= 0.962 kW+0.569 kW= 1.53 kW

Conclusion: Hence,the total thermal current is 1.53kW

(c)

To determine

To Calculate:The thermal resistance of two cube combination.

(c)

Expert Solution
Check Mark

Answer to Problem 37P

The equivalent thermal resistance is 0.052 K/W.

Explanation of Solution

Given:The temperature difference ΔT is 80°C and thermal current (I) is 1.53kW

Formula used:

The equivalent thermal resistance is obtained by:

  Req=ΔTI

Where, ΔT is the temperature difference and I is the thermal current.

Calculation:

Substitute the values and solve:

  Req=80K1.53kW= 52.28K/kW( 1.0kW 1000 W)=0.05228 K/W

Hence, the equivalent thermal resistance is 0.052 K/W .

Conclusion:Equivalent thermal resistance can be calculated using temperature difference and thermal current.

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