Import Question JSON

Current Question (ID: 10744)

Question:

$\text{50 g of ice at } 0°\text{C is dropped in a calorimeter of negligible heat capacity containing 50 g of water at } 100°\text{C, then the final temperature } (T_m) \text{ of the mixture will be: (neglect the heat loss)}$

Options:

1. $10°\text{C}$ (Correct)
2. $\text{Below } 0°\text{C}$
3. $20°\text{C}$
4. $\text{Above } 20°\text{C}$

Solution:

$\text{Hint: Heat is transferred from water to ice and no heat is required to heat up the calorimeter.}$ $\text{Step 1: Given that}$ $L_f = 80 \text{ cal/g}$ $C_W = 1 \text{ cal/g·°C}$ $\text{50 g water } 100°\text{C + 50 g ice } 0°\text{C}$ $\text{Step 2: Find heat required by ice}$ $Q_1 = mL_f$ $= 50 \times 80$ $= 4000 \text{ cal}$ $\text{Step 3: Find heat required by water}$ $Q_2 = mC \Delta T$ $= 50 \times 1 \times 100$ $= 5000 \text{ cal}$ $\text{Step 4: Calculate the required temperature}$ $\text{Let final temperature be T°C}$ $50 \times 1 \times (100 - T) = 4000 + 50 \times 1 \times (T - 0)$ $\Rightarrow T = 10°\text{C}$

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
}