Import Question JSON

Current Question (ID: 10748)

Question:

$\text{The two ends of a metal rod are maintained at temperatures } 100°\text{C and } 110°\text{C. The rate of heat flow in the rod is found to be } 4.0 \text{ J/s. If the ends are maintained at temperatures } 200°\text{C and } 210°\text{C, the rate of heat flow will be:}$

Options:

1. $44.0 \text{ J/s}$
2. $16.8 \text{ J/s}$
3. $8.0 \text{ J/s}$
4. $4.0 \text{ J/s}$ (Correct)

Solution:

$\text{Here, } \Delta T_1 = 110 - 100 = 10°\text{C}$ $\frac{dQ_1}{dt} = 4 \text{ J/s}$ $\Delta T_2 = 210 - 200 = 10°\text{C}$ $\frac{dQ_2}{dt} = ?$ $\text{As the rate of heat flow is directly proportional to the temperature difference and the temperature difference in both the cases is same i.e. } 10°\text{C. So, the same rate of heat will flow in the second case}$ $\text{Hence, } \frac{dQ_2}{dt} = 4 \text{ J/s}$

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
}