Import Question JSON

Current Question (ID: 10760)

Question:

$\text{Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities } K \text{ and } 2K, \text{ respectively. The equivalent thermal conductivity of the slab will be:}$

Options:

1. $\frac{2}{6}K$
2. $\sqrt{2K}$
3. $3K$
4. $\frac{4}{3}K$ (Correct)

Solution:

\text{For a compound slab with materials in series, we need to find the equivalent thermal conductivity.} \text{Given: Two materials with thermal conductivities } K \text{ and } 2K\text{, each having thickness } l \text{For series connection, thermal resistances add: } R = R_1 + R_2 \text{Thermal resistance formula: } R = \frac{l}{kA} \text{For the equivalent system: } \frac{2l}{K_{eq} \cdot A} = \frac{l}{2K \cdot A} + \frac{l}{K \cdot A} \text{Simplifying: } \frac{2l}{K_{eq} \cdot A} = \frac{l}{2K \cdot A} + \frac{2l}{2K \cdot A} = \frac{3l}{2K \cdot A} \text{Therefore: } \frac{2}{K_{eq}} = \frac{3}{2K} \text{Solving for } K_{eq}\text{: } K_{eq} = \frac{2 \times 2K}{3} = \frac{4K}{3} \text{Hence, the equivalent thermal conductivity is } \frac{4K}{3}

Import JSON File

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
}