Import Question JSON

Current Question (ID: 11098)

Question:

$\text{An ideal gas heat engine operates in a Carnot cycle between 227°C and 127°C. It absorbs } 6 \times 10^4 \text{ cals of heat at higher temperatures. The amount of heat converted to work will be?}$

Options:

1. $4.8 \times 10^4 \text{ cals}$
2. $2.4 \times 10^4 \text{ cals}$
3. $1.2 \times 10^4 \text{ cals}$ (Correct)
4. $6 \times 10^4 \text{ cals}$

Solution:

$\eta = \frac{W}{Q} = 1 - \frac{T_2}{T_1} \Rightarrow W = Q \left( 1 - \frac{T_2}{T_1} \right)$ $\text{Given:}$ $T_1 = 227°\text{C} = 227 + 273 = 500 \text{ K}$ $T_2 = 127°\text{C} = 127 + 273 = 400 \text{ K}$ $Q = 6 \times 10^4 \text{ cals}$ $W = 6 \times 10^4 \times \left( 1 - \frac{400}{500} \right)$ $W = 6 \times 10^4 \times \left( 1 - 0.8 \right)$ $W = 6 \times 10^4 \times 0.2$ $W = 1.2 \times 10^4 \text{ cals}$

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
}