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Current Question (ID: 19640)

Question:

$\text{The temperature of body drops from } 60^\circ \text{C to } 40^\circ \text{C in } 7 \text{ min. The surrounding temperature is } 10^\circ \text{C.}$ $\text{The temperature of body drops from } 40^\circ \text{C to } T^\circ \text{C in } 7 \text{ min. The value of } T \text{ is:}$

Options:

1. $16^\circ \text{C}$
2. $20^\circ \text{C}$
3. $28^\circ \text{C}$
4. $36^\circ \text{C}$

Solution:

$\text{Hint: Apply Newton's law of cooling.}$ $\text{Step 1: Find the proportionality constant } k.$ $\text{By applying Newton's law of cooling we get;} \frac{\Delta T}{\Delta t} = k \left( \frac{T_1 + T_2}{2} - T_s \right)$ $\Rightarrow \frac{60 - 40}{7} = k \left( \frac{60 + 40}{2} - 10 \right)$ $\Rightarrow k = \frac{1}{14}$ $\text{Step 2: Find the temperature of the body } T^\circ \text{C.}$ $\text{Again, by applying Newton's law we get;} \frac{40 - T^\circ}{7} = k \left( \frac{40 + T^\circ}{2} - 10 \right)$ $\Rightarrow \frac{40 - T^\circ}{7} = \frac{1}{14} \left( \frac{40 + T^\circ}{2} - 10 \right)$ $\Rightarrow 4(40 - T^\circ) = 20 + T^\circ$ $\Rightarrow T^\circ = 28^\circ \text{C}$ $\text{Hence, option (3) is the correct answer.}$

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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
}