Physics · Thermal Properties Of Matter · NEET
Steady state means the temperature at every point of the rod has stopped changing with time. Early on, the hot end warms up the middle, the middle warms the far end, and temperatures keep rising. After enough time each point settles to a fixed value. From then on, the heat entering the hot end equals the heat leaving the cold end, so no heat is stored in the rod. Only in this state does the simple formula H = KA(T1 - T2)/L apply.
H is the rate of heat flow, also called heat current. Its unit is joule per second, which is the watt (W). It tells you how much heat crosses any section of the rod each second. If you want the total heat Q conducted in time t, multiply: Q = H x t. Students often forget the time factor and treat H as if it were total heat in joules.
The two ends are held at fixed temperatures by outside sources (like a furnace and ice). These sources keep supplying heat to one end and removing it from the other. So the difference (T1 - T2) is maintained forever, and heat keeps flowing. The rod would only reach one uniform temperature if you removed those sources and let it settle by itself.
For the magnitude of H, no. Heat always flows from hot to cold, so we simply use the positive difference (hotter temperature minus colder temperature). The formula H = KA(T1 - T2)/L gives a positive rate as long as you subtract the colder end from the hotter end. The minus sign version H = -KA dT/dx is only used when you track direction along a chosen x-axis.
The temperature gradient is (T1 - T2)/L, that is the temperature difference divided by the length. In steady state and for a uniform rod, temperature falls at a constant rate along the length, so the gradient is the same everywhere in the rod. Its unit is kelvin per metre (K/m). A point at distance x from the hot end has temperature T1 - (T1 - T2) x / L.
No conversion of the difference is needed. A temperature difference of, say, 100 degrees Celsius is exactly the same as a difference of 100 kelvin, because the two scales have the same size of degree. Since the formula only uses (T1 - T2), you may keep both ends in Celsius or both in Kelvin. Just do not mix the two scales.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
H = K A (T1 - T2) / L, where K is thermal conductivity, A is area of cross-section, L is length and (T1 - T2) is the temperature difference between the ends. H is measured in watts.
The SI unit of H is the watt (W), which is the same as joule per second (J/s). It is the rate at which heat energy crosses a section of the rod.
It increases with larger thermal conductivity K, larger cross-section area A, and larger temperature difference (T1 - T2). It decreases with longer length L. It does not depend on time once steady state is reached.
K is a fixed property of the material (unit W per metre per kelvin) that says how good a conductor it is. H is the actual heat flowing per second through a particular rod (unit watt), and it depends on K plus the rod's size and the temperature difference.
Total heat Q = H x t = K A (T1 - T2) t / L. Here t is the time in seconds, so Q comes out in joules.
