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Current Question (ID: 10770)

Question:

$\text{Heat is flowing through a conductor of length } l \text{ from } x = 0 \text{ to } x = L. \text{ If its thermal resistance per unit length is uniform, which of the subsequent graphs is accurate?}$

Options:

1. $\text{Graph showing linear increase in temperature with position}$
2. $\text{Graph showing linear increase in temperature with position (steeper slope)}$
3. $\text{Graph showing linear decrease in temperature with position}$ (Correct)
4. $\text{Graph showing exponential decrease in temperature with position}$

Solution:

\text{Hint: } H = KA\frac{\Delta T}{L} \text{Step: Find the correct graph} \text{The heat current flowing through the conductor is given by:} H = KA\frac{\Delta T}{L} H = \frac{dQ}{dt} = -KA\frac{dT}{dx} \text{As the quantities } \frac{dQ}{dt}, K \text{ and } A \text{ are constant throughout the conductor:} \Delta T \propto -dx \text{Therefore, if distance increases, temperature decreases at a constant rate.} \text{Temperature decreases linearly with } x. \text{Hence, option (3) 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
}