Import Question JSON

Current Question (ID: 10815)

Question:

$\text{Consider two hot bodies, B}_1 \text{ and B}_2 \text{ which have temperatures of 100°C and 80°C respectively at t=0. The temperature of the surroundings is 40°C. The ratio of the respective rates of cooling R}_1 \text{ and R}_2 \text{ of these two bodies at t = 0 will be:}$

Options:

1. $\text{R}_1 : \text{R}_2 = 3 : 2$ (Correct)
2. $\text{R}_1 : \text{R}_2 = 5 : 4$
3. $\text{R}_1 : \text{R}_2 = 2 : 3$
4. $\text{R}_1 : \text{R}_2 = 4 : 5$

Solution:

\text{Hint: Initially at } t = 0 \text{, Rate of cooling (R) } \propto \text{ Fall in temperature of body } (\theta - \theta_0) \Rightarrow \frac{R_1}{R_2} = \frac{\theta_1 - \theta_0}{\theta_2 - \theta_0} = \frac{100 - 40}{80 - 40} = \frac{3}{2}

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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
}