Import Question JSON

Current Question (ID: 11095)

Question:

$\text{The efficiency of an ideal heat engine (Carnot heat engine) working between the freezing point and boiling point of water is:}$

Options:

1. $26.8\%$ (Correct)
2. $20\%$
3. $6.25\%$
4. $12.5\%$

Solution:

$\text{Hint: } \eta = 1 - \frac{T_L}{T_H}$ $\text{Step: Find the efficiency of the Carnot engine.}$ $\text{The efficiency of the engine is given by:}$ $\eta = 1 - \frac{T_L}{T_H}$ $\text{Where } T_L = 273 \text{ K (freezing point) and } T_H = 373 \text{ K (boiling point)}$ $\eta = 1 - \left(\frac{273}{373}\right)$ $\Rightarrow \eta = \left(\frac{100}{373}\right) \approx 0.268 = 26.8\%$ $\text{Hence, option (1) is the correct answer.}$

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
}