Concept explainers
(a)
Find the outdoor-indoor temperature difference in degrees Fahrenheit.
(a)
Answer to Problem 20P
The outdoor-indoor temperature difference is
Explanation of Solution
Given data:
The inside room temperature
The outside air temperature
Calculation:
The difference between the outdoor-indoor temperatures is,
Substitute
Thus, the outdoor-indoor temperature difference is
Conclusion:
Hence, the outdoor-indoor temperature difference is
(b)
Find the outdoor-indoor temperature difference in degrees Rankine.
(b)
Answer to Problem 20P
The outdoor-indoor temperature difference is
Explanation of Solution
Given data:
The inside room temperature
The outside air temperature
Formula used:
Formula to calculate the outdoor temperature in degrees Rankine is,
Here,
Formula to calculate the indoor temperature in degrees Rankine is,
Here,
Calculation:
Substitute
The outside temperature is
Substitute
The inside temperature is
Substitute
Thus, the outdoor-indoor temperature difference is
Conclusion:
Hence, the outdoor-indoor temperature difference is
(c)
Find the outdoor-indoor temperature difference in degrees Celsius.
(c)
Answer to Problem 20P
The outdoor-indoor temperature difference is
Explanation of Solution
Given data:
The inside room temperature
The outside air temperature
Formula used:
Formula to calculate the outdoor temperature in degrees Celsius is,
Here,
Formula to calculate the indoor temperature in degrees Celsius is,
Here,
Calculation:
Substitute
The outside temperature is
Substitute
The inside temperature is
Substitute
Thus, the outdoor-indoor temperature difference is
Conclusion:
Hence, the outdoor-indoor temperature difference is
(d)
Find the outdoor-indoor temperature difference in Kelvin.
(d)
Answer to Problem 20P
The outdoor-indoor temperature difference is
Explanation of Solution
Given data:
The inside room temperature
The outside air temperature
Formula used:
Formula to calculate the outdoor temperature in Kelvin is,
Here,
Formula to calculate the indoor temperature in Kelvin is,
Here,
Calculation:
Refer from part (c),
The inside room temperature
The outside air temperature
Substitute
The outside temperature is
Substitute
The inside temperature is
Substitute
Thus, the outdoor-indoor temperature difference is
Conclusion:
Hence, the outdoor-indoor temperature difference is
(e)
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)
Explanation of Solution
Case 1:
Refer to part (c),
The outdoor-indoor temperature difference is
Refer to part (d),
The outdoor-indoor temperature difference is
From part (c) and part (d), outdoor-indoor temperature differences are equal.
Note:
Let the temperature difference in Kelvin is,
Formula to calculate the temperature in degree Celsius is,
Here,
Substitute
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
Refer to part (b),
The outdoor-indoor temperature difference is
From part (a) and part (b), outdoor-indoor temperature differences are equal.
Note:
Let the temperature difference in Rankine is,
Formula to calculate the temperature in Rankine is,
Here,
Substitute
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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