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Current Question (ID: 20218)

Question:

$\text{One kg of water, at } 20^\circ \text{C, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of } 20 \, \Omega. \text{ The rms voltage in the mains is } 200 \, \text{V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to:}$ $\text{[Specific heat of water = } 4200 \, \text{J/(kg } ^\circ \text{C), Latent heat of water = } 2260 \, \text{kJ/kg]}$

Options:

1. $\text{10 minutes}$
2. $\text{22 minutes}$
3. $\text{3 minutes}$
4. $\text{16 minutes}$

Solution:

$\text{Hint: Power(time)=total energy required.}$ $R = \frac{V^2}{P} = \frac{200 \times 200}{20} = 2000 \, \text{watt}$ $V = 200 \, \text{V}$ $1 \, \text{kg water } 20^\circ \text{C} \rightarrow 1 \, \text{kg water } 100^\circ \text{C}$ $\text{Heat required } Q_1 = ms\Delta T = (1)(4200)(80) = 336000$ $1 \, \text{kg water } 100^\circ \text{C} \rightarrow 1 \, \text{kg vapour}$ $\text{Heat required } Q_2 = mL = (1) \, 2260 \times 1000 = 2260000$ $\text{(power) (time) = total heat required}$ $= 2000 \times \text{time} = 2260000 + 336000$ $\text{time} = 1298 \, \text{sec.}$ $\text{time} = 21.63 \, \text{mint.} \simeq 22 \, \text{minute}$

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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
}