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Current Question (ID: 10764)

Question:

$\text{A wall is made up of two layers, A and B. The thickness of the two layers is the same, but the materials are different. The thermal conductivity of A is double that of B. If in thermal equilibrium, the temperature difference between the two ends is } 36^\circ\text{C, then the difference in temperature between the two surfaces of A will be:}$

Options:

1. $6^\circ\text{C}$
2. $12^\circ\text{C}$ (Correct)
3. $18^\circ\text{C}$
4. $24^\circ\text{C}$

Solution:

\text{Suppose thickness of each wall is } x \text{ then} \text{For thermal equilibrium, the rate of heat transfer through both layers must be equal:} \left(\frac{Q}{t}\right)_{\text{combination}} = \left(\frac{Q}{t}\right)_A \frac{K_s A (\theta_1 - \theta_2)}{2x} = \frac{2KA (\theta_1 - \theta)}{x} \text{The equivalent thermal conductivity for the composite wall:} K_s = \frac{2 \times 2K \times K}{2K + K} = \frac{4K}{3} \text{and } (\theta_1 - \theta_2) = 36° \text{Substituting values:} \frac{\frac{4}{3}KA \times 36}{2x} = \frac{2KA (\theta_1 - \theta)}{x} \text{Solving for the temperature difference across wall A:} \text{Hence temperature difference across wall A is } (\theta_1 - \theta) = 12°\text{C}

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}