Revision

Midterm

Date2026-11-10
Modules1
Synthetic Course: written to test the Site template, from no Professor's material

01Thermal resistance

A wall resists heat like a resistor resists current

In steady conduction through a plane wall, the heat rate is set by the temperature drop across the wall and by the wall’s thermal resistance:

Q˙=ΔTR,R=LkA\dot{Q} = \frac{\Delta T}{R}, \qquad R = \frac{L}{k A}

A thicker wall (larger LL) resists more; a better conductor (larger kk) or a larger face (larger AA) resists less. Layers in series add their resistances, Rtotal=∑RiR_\text{total} = \sum R_i, and the same Q˙\dot{Q} passes through every layer.

الجدار يقاوم سريان الحرارة كما يقاوم المقاوم سريان التيار: فرق درجات الحرارة يدفعها، والمقاومة R=LkAR = \frac{L}{kA} تحدّ منها. في الشكل جدار سمكه 0.2 م تهبط حرارته من 20 إلى 5 درجات في خط مستقيم.
Assumed
supplied here, not in the Materials: x=0x = 0 · L=0.2 mL = 0.2\ \text{m} · T1=20T_1 = 20 · T2=5 ∘CT_2 = 5\ ^\circ\text{C}
−0.100.000.100.200510152025TT (°C)xx (m)T1T_1T2T_2
Fig.An illustrative wall 0.2 m0.2\ \text{m} thick; the temperature falls in a straight line
Rules

  1. Heat rate through a wall

    First, once the wall's resistance is known.

    Q˙=ΔTR\dot{Q} = \frac{\Delta T}{R}

  2. Resistance of a plane wall

    For each layer, from its thickness, conductivity and face.

    R=LkAR = \frac{L}{k A}

  3. Layers in series

    When layers are stacked and the same heat passes through each.

    Rtotal=∑RiR_\text{total} = \sum R_i