Physics · Thermal Properties Of Matter · NEET
The maths is identical, only the names change. In electricity: current I = V / R, where V is the potential difference. In heat flow: heat current H = (delta T) / R_thermal, where delta T is the temperature difference. So temperature difference behaves like voltage, the flow of heat per second behaves like current, and R_thermal = L/(K A) behaves like the resistor. Once you see this, every rod problem becomes a simple circuit problem.
R = L / (K A). Here L is the length of the rod (in the direction heat flows), A is the cross-section area, and K is the thermal conductivity of the material. A long thin rod has high resistance (small heat flow). A short fat rod of good conductor has low resistance (large heat flow). The SI unit of R is kelvin per watt (K/W).
K measures how well a material lets heat pass. Metal has high K, so it conducts heat easily, meaning it resists heat flow very little. In the formula R = L/(K A), K is in the denominator, so a large K makes R small. Think of it like electrical conductivity: better conductor equals lower resistance.
Yes. For rods joined end to end (series), the same heat current H passes through each, so R_total = R1 + R2 + R3 + ... For rods placed side by side (parallel), the temperature difference is the same across each, so you add the reciprocals: 1/R_total = 1/R1 + 1/R2 + ... These are the exact rules you already know from electric circuits.
In steady state the heat current H is the same everywhere in a series chain. First find H = (T_hot - T_cold) / R_total. Then the junction temperature equals the hot end minus the drop across the first resistor: T_junction = T_hot - H x R1. This is just like finding the voltage at a node using V = I x R across one resistor.
Three identical rods are connected in series (end to end). The two outer rods have thermal conductivity 2K and the middle rod has conductivity K. Each rod has length L and area A. The left end is kept at 3T and the right end at T, with the sides insulated. If T1 is the temperature of the left junction and T2 of the right junction, the ratio T1 : T2 is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Kelvin per watt (K/W), because R = (temperature difference) / (heat current), and heat current is measured in watts.
Temperature difference delta T is like voltage V. Heat current H (joules per second) is like electric current I. Thermal resistance R = L/KA is like electrical resistance R = rho L/A. And H = delta T / R is like I = V / R.
It applies in the steady state, when temperatures no longer change with time and the same heat current flows through the whole chain. It also assumes the sides of the rods are insulated so heat only flows along the length.
Series (end to end): same heat current, so R_total = R1 + R2 + ... . Parallel (side by side): same temperature difference, so 1/R_total = 1/R1 + 1/R2 + ... . Identical to resistor rules.
More. A larger area A makes R = L/(K A) smaller, so for the same temperature difference the heat current H = delta T / R is larger.
