Import Question JSON

Current Question (ID: 19673)

Question:

$\text{If minimum possible work is done by a refrigerator in converting 100 grams of water at } 0^\circ \text{C to ice, how much heat (in calories) is released to the surroundings at temperature } 27^\circ \text{C (Latent heat of ice = 80 cal/gram) to the nearest integer?}$ $1. \ 3242$ $2. \ 8791$ $3. \ 1634$ $4. \ 100$

Options:

1. $3242$
2. $8791$
3. $1634$
4. $100$

Solution:

$\text{Hint: C.O.P } = \frac{Q_{\text{abs}}}{Q_{\text{rej}} - Q_{\text{abs}}} = \frac{T_{\text{source}}}{T_{\text{sink}} - T_{\text{source}}}.$ $w + Q_1 = Q_2$ $w = Q_2 - Q_1$ $C.O.P = \frac{Q_1}{w} = \frac{Q_1}{Q_2 - Q_1} = \frac{273}{300 - 273} = \frac{Q_1}{W}$ $w = \frac{27}{273} \times 80 \times 100 \times 4.2$ $Q_2 = w + \theta_1$ $Q_2 = \frac{27}{273} \times 300 \times 4.2 + 80 \times 100 \times 4.$ $Q_2 = \frac{27}{273} \times 80 \times 100 = 8791.2 \text{ cal}$

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
}