Import Question JSON

Current Question (ID: 10743)

Question:

$\text{Some water at } 0°\text{C is placed in a large insulated enclosure (vessel). The water vapour formed is pumped out continuously. What fraction of the water will eventually freeze, if the latent heat of vaporization is seven times the latent heat of fusion?}$

Options:

1. $\frac{7}{8}$ (Correct)
2. $\frac{8}{7}$
3. $\frac{3}{8}$
4. $\frac{5}{8}$

Solution:

$\text{Given:}$ $m = \text{mass of water, } f = \text{fraction which freezes}$ $L_1 = \text{latent heat of vaporization}$ $L_2 = \text{latent heat of fusion, } L_1 = 7L_2$ $\text{Mass of water frozen} = mf$ $\text{Heat lost by freezing water} = mfL_2$ $\text{Mass of vapour formed} = m(1 - f)$ $\text{Heat gained by vapour} = m(1 - f)L_1$ $\text{For equilibrium (heat lost = heat gained):}$ $mfL_2 = m(1 - f) \times 7L_2$ $f = 7(1 - f)$ $f = 7 - 7f$ $f + 7f = 7$ $8f = 7$ $f = \frac{7}{8}$

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
}