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Current Question (ID: 10496)

Question:

$\text{A certain number of spherical drops of a liquid of radius } r \text{ coalesce to form a single drop of radius } R \text{ and volume } V\text{. If } T \text{ is the surface tension of the liquid, then: Energy} = 4VT\left(\frac{1}{r} - \frac{1}{R}\right) \text{ is released}$

Options:

1. $\text{Energy} = 4VT\left(\frac{1}{r} - \frac{1}{R}\right) \text{ is released}$
2. $\text{Energy} = 3VT\left(\frac{1}{r} + \frac{1}{R}\right) \text{ is released}$
3. $\text{Energy} = 3VT\left(\frac{1}{r} - \frac{1}{R}\right) \text{ is released}$
4. $\text{Energy is neither released nor absorbed}$

Solution:

\text{If the surface area changes, it will change the surface energy as well.} \text{As the surface area is decreasing, energy will be released.} \text{Change in surface energy} = T \times \Delta A \text{If there is } n \text{ no. of small drops:} \text{Volume of a large drop = volume of } n \text{ small drops} \frac{4}{3}\pi R^3 = n \times \frac{4}{3}\pi r^3 \text{Change in area:} \Delta A = 4\pi R^2 - n \times 4\pi r^2 \Delta A = 3V\left(\frac{1}{r} - \frac{1}{R}\right) E = T \times \Delta A = 3VT\left(\frac{1}{r} - \frac{1}{R}\right) \text{ released}

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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
}