การนำความร้อน – ปัญหาและแนวทางแก้ไข
1. Two metals have the same size but different type. The thermal conductivity of P = 2 times the thermal conductivity of Q. What is the อุณหภูมิ between the two metals, as shown in the figure below.
เป็นที่รู้จัก :
kQ = เค
kP = 2k
ต้องการ: Temperature between the two metals
วิธีการแก้ปัญหา:
สมการของ การนำความร้อน :
Q/t = The rate of the heat conduction, k = thermal conductivity, A = the cross-sectional area of the object, T1 = high temperature, T2 = low temperature, l = the length of metal.
Temperature = 60 oC.
2. Metal A and metal B have the same length and the same cross-sectional. If the thermal conductivity of metal A = ¼ times the thermal conductivity of metal B. Both metals heated at its end and the change in temperature of both metals are the same. The ratio of the rate of the heat conduction of metal A to metal B.
เป็นที่รู้จัก :
The cross-sectional of A (A) = The cross-sectional B (A)
The length of A (l) = the length of B (l)
The thermal conductivity of metal B (kB) = เค
The thermal conductivity of metal A (kA) = ¼ k
The change in temperature of metal A (ΔT) = the change in temperature of metal B (ΔT)
ต้องการ: The ratio of the rate of the heat conduction
วิธีการแก้ปัญหา:
สมการการนำความร้อน:
Q/t = the rate of the heat conduction, k = การนำความร้อน, A = พื้นที่หน้าตัด, T2 = อุณหภูมิสูง, T1 = อุณหภูมิต่ำ, l = length of metal
3. Two metals, A and B, have the same size. The thermal conduction of the metal A = 2k and the thermal conduction of the metal B = k.
As shown in the figure below, the end of both metals has the different temperature.
What is the temperature between both metals?
เป็นที่รู้จัก :
Two metals, A and B, have the same size.
The thermal conductivity of metal A = 2k
The thermal conductivity of metal B = k
The temperature of one end of metal A = 210oC
The temperature of one end of metal B = 30oC
ต้องการ: Temperature between metal A and B
วิธีการแก้ปัญหา:
The equation of the rate of the heat conduction :
Q/t = the rate of the heat conduction, k = the thermal conductivity, A = พื้นที่หน้าตัด, T1-T2 = การเปลี่ยนแปลงของอุณหภูมิ, l = length of metal
The temperature between P and Q :
4. Two metals have the same size. The thermal conductivity of metal II = 2 times the thermal conductivity of metal I. If one end of metal I is heated so T1 = 100 oC and one end of metal II is heated so T2 = 25 oC , then what is the temperature between both metals.
เป็นที่รู้จัก :
The heat conductivity of metal I = k
The heat conductivity of metal II = 2k
The temperature at one end of metal I = 100oC
The temperature at one end of metal II = 25oC
ต้องการ: Temperature between metal I and II
วิธีการแก้ปัญหา:
สมการการนำความร้อน:
Q/t = the rate of the heat conduction, k = the thermal conductivity, A = พื้นที่หน้าตัด, T1-T2 = การเปลี่ยนแปลงของอุณหภูมิ, l = the length of metal
Temperature between both metals :
Temperature between metal I and II is 50oC.
5. Metal rods of the same size, but made of different metals are combined as shown in the figure below. If the thermal conductivity of metal I = 4 times the metal conductivity II, then the temperature at the junction of the two metals is ……
เป็นที่รู้จัก :
The thermal conductivity of metal I = 4k
The thermal conductivity of metal I = เค
The temperature of one end of the metal I = 50oC
The temperature of one end of the metal II = 0oC
ต้องการ: the temperature at the junction of the two metals
วิธีการแก้ปัญหา:
The equation of the heat transfer conduction :
Q/t = the rate of the heat conduction, k = การนำความร้อน, A = พื้นที่หน้าตัด, T2 = อุณหภูมิสูง, T1 = อุณหภูมิต่ำ, T1-T2 = The change in temperature, ล = length of metal
Both metals have the same size so that A and I eliminated from the equation :
6. The following figure shows different A and B metal rods connected at one end.
The cross-sectional area of both rods is the same, but the length of A is twice the length of B and the thermal conduction coefficient A is 3 times B. If the free ends A and B are subjected to different temperature, the temperature at the junction is …
เป็นที่รู้จัก :
The thermal conductivity of metal เอ = 3k
The thermal conductivity of metal B = เค
Length of metal A = 2l
Length of metal B = l
The temperature of one end metal A = 100oC
The temperature of one end metal B = 40oC
ต้องการ: The temperature at the junction
วิธีการแก้ปัญหา:
The equation of the heat transfer conduction :
Q/t = the rate of the heat conduction, k = การนำความร้อน, A = พื้นที่หน้าตัด, T2 = อุณหภูมิสูง, T1 = อุณหภูมิต่ำ, T1-T2 = The change in temperature, ล = length of metal
Both rods have the same size so that A eliminated from the equation.
