Import Question JSON

Current Question (ID: 11094)

Question:

$\text{The efficiency of a Carnot heat engine working between the temperatures } 27°\text{C and } 227°\text{C is:}$

Options:

1. $0.1$
2. $0.6$
3. $0.2$
4. $0.4$ (Correct)

Solution:

$\text{Hint: } \eta = 1 - \frac{T_2}{T_1}$ $\text{Step 1: Determine the source and sink temperatures in kelvin.}$ $T_1 = 500 \text{ K}$ $T_2 = 300 \text{ K}$ $\text{Step 2: Find the efficiency of the Carnot engine.}$ $\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{300}{500} = 0.4$

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
}