Import Question JSON

Current Question (ID: 10742)

Question:

$\text{In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at 150°C is dropped in a copper calorimeter (of water equivalent of 0.025 kg) containing 150 cm}^3 \text{ of water at 27°C. The final temperature is 40°C. The specific heat of the metal will be:}$ $\text{(Heat losses to the surroundings are negligible)}$

Options:

1. $0.40 \text{ Jg}^{-1}\text{K}^{-1}$
2. $0.43 \text{ Jg}^{-1}\text{K}^{-1}$ (Correct)
3. $0.54 \text{ Jg}^{-1}\text{K}^{-1}$
4. $0.61 \text{ Jg}^{-1}\text{K}^{-1}$

Solution:

$\text{Hint: Heat loss = heat gain.}$ $\text{Step 1: Calculate the specific heat of the metal.}$ $\text{Heat lost = Heat gained by (calorimeter + water)}$ $m_s c_s \Delta T_s = m_w c_w \Delta T_c + C_c \Delta T_c$ $200 \times c_s \times [150 - 40] = 150 \times 4.2 \times 13 + 25 \times 4.2 \times 13$ $c_s = \frac{175 \times 4.2 \times 13}{110 \times 200} = 0.43 \text{ J g}^{-1} \text{K}^{-1}$

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
}