Import Question JSON

Current Question (ID: 10786)

Question:

$\text{A pan filled with hot food cools in 2 minutes from } 94°\text{C to } 86°\text{C when the room temperature is } 20°\text{C. How long will it take to cool from } 71°\text{C to } 69°\text{C?}$

Options:

1. $50 \text{ s}$
2. $52 \text{ s}$
3. $42 \text{ s}$ (Correct)
4. $48 \text{ s}$

Solution:

$\text{Hint: Apply Newton's law of cooling.}$ $\text{Step 1: Find the initial rate of cooling.}$ $\text{From Newton's law of cooling, we have:}$ $\frac{\text{Change in temperature}}{\text{Time}} = K \Delta T$ $\Rightarrow \frac{8°\text{C}}{2 \text{ min}} = K(70)°\text{C} \ldots\ldots\ldots(1)$ $\text{Step 2: Find the final rate of cooling.}$ $\frac{2°\text{C}}{\text{Time}} = K(50)°\text{C} \ldots\ldots\ldots(2)$ $\text{Step 3: Find the time of cooling in the second case.}$ $\text{When we divide the above two equations, we have:}$ $\frac{8°\text{C}/2 \text{ min}}{2°\text{C}/\text{Time}} = \frac{K(70)°\text{C}}{K(50)°\text{C}}$ $\Rightarrow \text{Time} = 0.7 \text{ min} = 42 \text{ s}$

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
}