Import Question JSON

Current Question (ID: 19638)

Question:

$\text{The temperature of hot soup in a bowl goes } 98^\circ \text{C to } 86^\circ \text{C in 2 min.}$ $\text{The temperature of the surrounding is } 22^\circ \text{C.}$ $\text{What is the time taken for the temperature of the soup to go from } 75^\circ \text{C to } 69^\circ \text{C?}$ $\text{(Assume Newton's law of cooling is valid)}$

Options:

1. $1 \text{ min}$
2. $1.4 \text{ min}$
3. $2 \text{ min}$
4. $3.2 \text{ min}$

Solution:

$\frac{\Delta \theta}{\Delta t} = -K \left( \frac{\theta_1 + \theta_2}{2} - \theta_0 \right)$ $\text{Given, } \theta_0 = 22^\circ \text{C}$ $\frac{98 - 96}{2} = -K \left( \frac{98 + 86}{2} - 22 \right) \quad \cdots (1)$ $\frac{75 - 69}{t_2} = -K \left( \frac{75 + 69}{2} - 22 \right) \quad \cdots (2)$ $\text{From (1) and (2)}$ $t_2 = \frac{70}{50} = 1.4 \text{ min}$

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
}