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Current Question (ID: 10750)

Question:

$\text{Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod has the same length. The left and right ends are kept at } 0°\text{C and } 90°\text{C, respectively. The temperature at the junction of the three rods will be:}$

Options:

1. $45°\text{C}$
2. $60°\text{C}$ (Correct)
3. $30°\text{C}$
4. $20°\text{C}$

Solution:

$\text{Hint: The rate of heat flow is identical to the electric current.}$ $\text{Step 1: Find the thermal resistance.}$ $R_T = \frac{1}{kA}$ $\text{Step 2: Apply Kirchoff's junction law.}$ $i = \frac{\Delta T}{R}$ $i_1 = \frac{90 - \theta}{R} = i_2$ $i_3 = \frac{\theta - 0}{R}$ $i_1 + i_2 = i_3$ $\frac{90 - \theta}{R} + \frac{90 - \theta}{R} = \frac{\theta}{R}$ $\Rightarrow \theta = 60°\text{C}$

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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
}