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Current Question (ID: 19632)

Question:

$\text{Two metallic blocks } M_1 \text{ and } M_2 \text{ of the same area of the cross-section are connected to each other (as shown in the figure). If the thermal conductivity of } M_2 \text{ is } K, \text{ then the thermal conductivity of } M_1 \text{ will be:}$ $\text{(Assume steady state heat conduction)}$

Options:

1. $10K$
2. $8K$
3. $12.5K$
4. $2K$

Solution:

$\text{Hint: } \Delta T \propto \frac{l}{K}$ $\text{Step: Find the thermal conductivity of the block.}$ $\text{Let the thermal conductivity of } M_1 \text{ is } x.$ $\text{In a steady state, the thermal current in both blocks is the same}$ $i.e., \ i_1 = i_2 \ \left( i = \frac{K A \Delta T}{L} \right)$ $\Rightarrow \frac{x(100-80)A}{16} = \frac{K(80-0)A}{8}$ $\Rightarrow x = \frac{2 \times 80}{20} K = 8K$ $\text{Hence, option (2) is the correct answer.}$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}