Import Question JSON

Current Question (ID: 11093)

Question:

$\text{A heat engine operates between the temperatures of 300 K and 500 K. If it extracts 1200 J of heat energy from the source, then the maximum amount of work that can be done by the engine is:}$

Options:

1. $720 \text{ J}$
2. $520 \text{ J}$
3. $480 \text{ J}$ (Correct)
4. $200 \text{ J}$

Solution:

$\text{Hint: Use the formula of Efficiency of Carnot engine.}$ $\text{Step 1: Efficiency of Carnot Engine:}$ $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q}$ $\text{Step 2: Put the values in above formula.}$ $\text{Given: } T_1 = 500 \text{ K, } T_2 = 300 \text{ K, } Q = 1200 \text{ J}$ $1 - \frac{300}{500} = \frac{W}{1200}$ $\frac{200}{500} = \frac{W}{1200}$ $W = \frac{200 \times 1200}{500} = 480 \text{ J}$

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
}