Import Question JSON

Current Question (ID: 19723)

Question:

$\text{In a Carnot engine, the temperature of the reservoir is } 527^\circ \text{C and that of the sink is } 200 \text{ K.}$ $\text{If the work done by the engine when it transfers heat from the reservoir to sink is } 12000 \text{ kJ, the quantity of heat absorbed by the engine from the reservoir is:}$

Options:

1. $12 \times 10^6 \text{ J}$
2. $14 \times 10^6 \text{ J}$
3. $16 \times 10^6 \text{ J}$
4. $18 \times 10^6 \text{ J}$

Solution:

$\text{The efficiency of a Carnot engine is given by } \eta = 1 - \frac{T_2}{T_1}$ $\text{where } T_1 = 527^\circ \text{C} = 800 \text{ K and } T_2 = 200 \text{ K.}$ $\eta = 1 - \frac{200}{800} = \frac{3}{4}$ $\text{The work done } W = 12000 \text{ kJ} = 12 \times 10^6 \text{ J}$ $\text{The heat absorbed } Q_1 = \frac{W}{\eta} = \frac{12 \times 10^6}{\frac{3}{4}} = 16 \times 10^6 \text{ J}$

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
}