Import Question JSON

Current Question (ID: 10796)

Question:

$\text{One kilogram of ice at } 0^\circ\text{C is mixed with one kilogram of water at } 80^\circ\text{C. The final temperature of the mixture will be: (Take: Specific heat of water } = 4200 \text{ J kg}^{-1}\text{K}^{-1}\text{, latent heat of ice} = 336 \text{ kJ kg}^{-1}\text{)}$

Options:

1. $0^\circ\text{C}$ (Correct)
2. $50^\circ\text{C}$
3. $40^\circ\text{C}$
4. $60^\circ\text{C}$

Solution:

$\text{Let } \theta^\circ \text{ be the temperature of the mixture.}$ $\text{Using the principle of calorimetry,}$ $\text{Heat gained by the ice} = \text{Heat lost by the water}$ $1 \times 336 \times 10^3 + 1 \times 4200 \times \theta = 1 \times 4200 \times (80 - \theta)$ $2 \times 4200 \times \theta = 4200 \times 80 - 336 \times 10^3 = (336 - 336) \times 10^3$ $\theta = 0^\circ\text{C}$

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
}