Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN: 9781305084766
Author: Saeed Moaveni
Publisher: Cengage Learning
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Chapter 6, Problem 20P

(a)

To determine

Find the outdoor-indoor temperature difference in degrees Fahrenheit.

(a)

Expert Solution
Check Mark

Answer to Problem 20P

The outdoor-indoor temperature difference is 42°F.

Explanation of Solution

Given data:

The inside room temperature (Tindoor) is 68°F.

The outside air temperature (Toutdoor) is 110°F.

Calculation:

The difference between the outdoor-indoor temperatures is,

ToutdoorTindoor (1)

Substitute 68°F for Tindoor and 110°F for Toutdoor in equation (1).

ToutdoorTindoor=110°F68°F=42°F

Thus, the outdoor-indoor temperature difference is 42°F.

Conclusion:

Hence, the outdoor-indoor temperature difference is 42°F.

(b)

To determine

Find the outdoor-indoor temperature difference in degrees Rankine.

(b)

Expert Solution
Check Mark

Answer to Problem 20P

The outdoor-indoor temperature difference is 42°R.

Explanation of Solution

Given data:

The inside room temperature (Tindoor) is 68°F.

The outside air temperature (Toutdoor) is 110°F.

Formula used:

Formula to calculate the outdoor temperature in degrees Rankine is,

Toutdoor(°R)=Toutdoor(°F)+459.67 (2)

Here,

Toutdoor(°R) is the outside temperature in degree Rankine.

Toutdoor(°F) is the outside temperature in degree Fahrenheit.

Formula to calculate the indoor temperature in degrees Rankine is,

Tindoor(°R)=Tindoor(°F)+459.67 (3)

Here,

Tindoor(°R) is the inside temperature in degree Rankine.

Tindoor(°F) is the inside temperature in degree Fahrenheit.

Calculation:

Substitute 110 for Toutdoor in equation (2).

Toutdoor(°R)=110°+459.67=569.67

The outside temperature is Toutdoor=569.67°R.

Substitute 68 for Tindoor in equation (3).

Tindoor(°R)=68+459.67=527.67

The inside temperature is Tindoor=527.67°R.

Substitute 527.67°R for Tindoor and 569.67°R for Toutdoor in equation (1).

ToutdoorTindoor=569.67°R527.67°R=42°R

Thus, the outdoor-indoor temperature difference is 42°R.

Conclusion:

Hence, the outdoor-indoor temperature difference is 42°R.

(c)

To determine

Find the outdoor-indoor temperature difference in degrees Celsius.

(c)

Expert Solution
Check Mark

Answer to Problem 20P

The outdoor-indoor temperature difference is 23.3°C.

Explanation of Solution

Given data:

The inside room temperature (Tindoor) is 68°F.

The outside air temperature (Toutdoor) is 110°F.

Formula used:

Formula to calculate the outdoor temperature in degrees Celsius is,

Toutdoor(°C)=59(Toutdoor(°F)32) (4)

Here,

Toutdoor(°C) is the outside temperature in degree Celsius.

Toutdoor(°F) is the outside temperature in degree Fahrenheit.

Formula to calculate the indoor temperature in degrees Celsius is,

Tindoor(°R)=59(Tindoor(°F)32) (5)

Here,

Tindoor(°C) is the inside temperature in degree Celsius.

Tindoor(°F) is the inside temperature in degree Fahrenheit.

Calculation:

Substitute 110 for Toutdoor in equation (4).

Toutdoor(°C)=59(11032)=43.3

The outside temperature is Toutdoor=43.3°C.

Substitute 68 for Tindoor in equation (5).

Tindoor(°C)=59(6832)=20

The inside temperature is Tindoor=20°C.

Substitute 20°C for Tindoor and 43.3°C for Toutdoor in equation (1).

ToutdoorTindoor=43.3°C20°C=23.3°C

Thus, the outdoor-indoor temperature difference is 23.3°C.

Conclusion:

Hence, the outdoor-indoor temperature difference is 23.3°C.

(d)

To determine

Find the outdoor-indoor temperature difference in Kelvin.

(d)

Expert Solution
Check Mark

Answer to Problem 20P

The outdoor-indoor temperature difference is 23.3°K.

Explanation of Solution

Given data:

The inside room temperature (Tindoor) is 68°F.

The outside air temperature (Toutdoor) is 110°F.

Formula used:

Formula to calculate the outdoor temperature in Kelvin is,

Toutdoor(K)=Toutdoor(°C)+273 (6)

Here,

Toutdoor(°C) is the outside temperature in degree Celsius.

Toutdoor(K) is the outside temperature in Kelvin.

Formula to calculate the indoor temperature in Kelvin is,

Tindoor(K)=Tindoor(°C)+273 (7)

Here,

Tindoor(°C) is the inside temperature in degree Celsius.

Tindoor(K) is the inside temperature in Kelvin.

Calculation:

Refer from part (c),

The inside room temperature (Tindoor) is 20°C.

The outside air temperature (Toutdoor) is 43.3°C.

Substitute 43.3 for Toutdoor in equation (6).

Toutdoor(K)=43.3+273=316.3

The outside temperature is Toutdoor=316.3K.

Substitute 20 for Tindoor in equation (7).

Tindoor(K)=20+273=293

The inside temperature is Tindoor=293K.

Substitute 293K for Tindoor and 316.3K for Toutdoor in equation (1).

ToutdoorTindoor=316.3K293K=23.3K

Thus, the outdoor-indoor temperature difference is 23.3°K.

Conclusion:

Hence, the outdoor-indoor temperature difference is 23.3°K.

(e)

To determine

Check whether one degree temperature difference in Celsius equal to one temperature difference in kelvin, and one degree temperature in Fahrenheit equal to one degree temperature difference in Rankine.

(e)

Expert Solution
Check Mark

Explanation of Solution

Case 1:

Refer to part (c),

The outdoor-indoor temperature difference is 23.3°C.

Refer to part (d),

The outdoor-indoor temperature difference is 23.3°K.

From part (c) and part (d), outdoor-indoor temperature differences are equal.

Note:

Let the temperature difference in Kelvin is,

T1(K)T2(K) (8)

Formula to calculate the temperature in degree Celsius is,

T(K)=T(°C)+273

Here,

T(K) is the temperature in Kelvin.

T(°C) is the temperature in degree Celsius.

Substitute T1(°C)+273 for T1(°R) and T2(°C)+273 for T2(°R) in equation (8).

T1(K)T2(K)=(T1(°C)+273)(T2(°C)+273)=T1(°C)+273T2(°C)273=T1(°C)T2(°C)

Thus, one degree temperature difference in Celsius is equal to one temperature difference in kelvin.

Case 2:

Refer to part (a),

The outdoor-indoor temperature difference is 42°F.

Refer to part (b),

The outdoor-indoor temperature difference is 42°R.

From part (a) and part (b), outdoor-indoor temperature differences are equal.

Note:

Let the temperature difference in Rankine is,

T1(°R)T2(°R) (9)

Formula to calculate the temperature in Rankine is,

T(°R)=T(°F)+459.67

Here,

T(°R) is the temperature in degree Rankine.

T(°F) is the temperature in degree Fahrenheit.

Substitute T1(°F)+459.67 for T1(°R) and T2(°F)+459.67 for T2(°R) in equation (9).

T1(°R)T2(°R)=(T1(°F)+459.67)(T2(°F)+459.67)=T1(°F)+459.67T2(°F)459.67=T1(°F)T2(°F)

Therefore, one degree temperature in Fahrenheit is equal to one degree temperature difference in Rankine.

Conclusion:

Hence, one degree temperature difference in Celsius equal to one temperature difference in kelvin, and one degree temperature in Fahrenheit equal to one degree temperature difference in Rankine has been explained.

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Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

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