Import Question JSON

Current Question (ID: 10501)

Question:

$\text{A liquid drop at temperature T, isolated from its surroundings, breaks into a number of droplets. The temperature of the droplets will be—}$

Options:

1. $\text{equal to T}$
2. $\text{greater than T}$
3. $\text{less than T}$
4. $\text{either (1), (2) or (3) depending on the surface tension of the liquid.}$

Solution:

$\text{The total surface area of the droplets is greater than that of a single drop. Hence, they have greater surface energy. This extra energy must be drawn from the internal energy of the drop.}$ $\text{When a liquid drop breaks into smaller droplets, the total surface area increases significantly. Since surface energy is proportional to surface area, the total surface energy of the system increases.}$ $\text{Since the system is isolated from its surroundings, energy conservation requires that this increase in surface energy must come from the internal energy of the liquid.}$ $\text{As internal energy decreases, the temperature of the droplets decreases below the original temperature T.}$ $\text{Therefore, the temperature of the droplets will be less than T.}$

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
}