Import Question JSON

Current Question (ID: 19642)

Question:

$\text{A copper ball of mass } 100 \text{ g is at a temperature } T. \text{ It is dropped into a copper calorimeter of mass } 100 \text{ g, containing } 170 \text{ g of water at room temperature. The final temperature of the system is found to be } 75^\circ\text{C. The initial temperature } T \text{ of the copper ball is:}$ $\text{(Given: room temperature } = 30^\circ\text{C, specific heat of copper } = 0.1 \text{ cal/g }^\circ\text{C)}$

Options:

1. $800^\circ\text{C}$
2. $885^\circ\text{C}$
3. $1250^\circ\text{C}$
4. $825^\circ\text{C}$

Solution:

$\text{Hint: Total heat gain = Total heat loss}$ $\text{Step: Find the initial temperature } T \text{ of the copper ball.}$ $Q_{\text{lost}} = Q_{\text{gain}}$ $\Rightarrow m_1s_1\Delta T_1 = m_2s_2\Delta T_2 + m_3s_3\Delta T_3$ $\Rightarrow 100 \times 0.1(T - 75) = 100 \times 0.1(75 - 30) + 170 \times 1 \times (75 - 30)$ $\Rightarrow T = 885^\circ\text{C}$ $\text{Hence, option (2) is the correct answer.}$

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
}