Import Question JSON

Current Question (ID: 19722)

Question:

$\text{A Carnot engine takes } 5000 \text{ kcal of heat from a reservoir at } 727^\circ\text{C}$ $\text{and gives heat to a sink at } 127^\circ\text{C. The work done by the engine is:}$

Options:

1. $3 \times 10^6 \text{ J}$
2. $\text{zero}$
3. $12.6 \times 10^6$
4. $8.4 \times 10^6$

Solution:

$\text{Hint: } \frac{Q_1}{Q_2} = \frac{T_1}{T_2}$ $\text{Step: Find the work done by the engine.}$ $\text{The efficiency of the engine is given by:}$ $\Rightarrow \eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$ $\text{Substitute the known values we get:}$ $\Rightarrow 1 - \frac{400}{1000} = \frac{W}{5000 \times 1000 \times 4.2} = 0.6$ $\text{The work done by the engine is given by:}$ $\Rightarrow W = 0.6 \times 5 \times 10^6 \times 4.2 = 12.6 \times 10^6 \text{ J}$ $\text{Hence, option (3) is the correct answer.}$

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
}