Import Question JSON

Current Question (ID: 19624)

Question:

$\text{Two materials having coefficients of thermal conductivity } 3K \text{ and } K \text{ and thickness } d \text{ and } 3d \text{ respectively, are joined to form a slab as shown in the figure.}$ $\text{The temperatures of the outer surfaces are } \theta_1 \text{ and } \theta_2 \text{ respectively, } (\theta_2 > \theta_1).$ $\text{The temperature at the interface is:}$

Options:

1. $\frac{\theta_2 + \theta_1}{2}$
2. $\frac{\theta_1}{2} + \frac{2\theta_2}{3}$
3. $\frac{\theta_1}{10} + \frac{9\theta_2}{10}$
4. $\frac{\theta_1}{6} + \frac{5\theta_2}{6}$

Solution:

$\text{Hint: In steady state heat current will be same.}$ $\text{Heat current will be same in both}$ $H_1 = H_2$ $\frac{3KA}{d}(\theta_2 - \theta) = \frac{KA}{3d}(\theta - \theta_1)$ $9\theta_2 - 9\theta = \theta - \theta_1$ $\theta = \frac{\theta_1}{10} + \frac{9\theta_2}{10}$

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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
}