Problem Statement
Analyze the circuit: Analyze the circuit: Two rods, one of copper ($k_1 = 400$ W/m·K, $L_1 = 0.1$ m) and one of steel ($k_2 = 50$ W/m·K, $L_2 = 0.2$ m), each of area $A = 10^{-4}$ m² are joined in series. The free ends are at 100°C and 0°C. Find the rate of heat flow and the interface temperature. $k_1 = 400$, $L_1 = 0.
Given Information
- See problem statement for all given quantities.
Physical Concepts & Formulas
Thermodynamics governs energy transformations involving heat and work. The First Law $\Delta U = Q – W$ expresses energy conservation. For an ideal gas, internal energy depends only on temperature ($U = nC_VT$), and the equation of state $PV = nRT$ links pressure, volume, and temperature.
- $\Delta U = Q – W$ — First Law of Thermodynamics
- $PV = nRT$ — ideal gas equation
- $C_P – C_V = R$, $\gamma = C_P/C_V$
- $W = \int P\,dV$ — work done by gas
Step-by-Step Solution
Step 1 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 2 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 3 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Worked Calculation
Full substitution shown in the steps above.
Answer
$$\boxed{I = \dfrac{\mathcal{E}}{R_{eq}+r}}$$
Physical Interpretation
The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.
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