Import Question JSON

Current Question (ID: 19694)

Question:

$300$ \text{ calories of heat is given to a heat engine and it rejects } 225 \text{ calories of heat. If source temperature is } 227^\circ \text{C, then the temperature of sink will be:}$ $1. \ 102^\circ \text{C}$ $2. \ 90^\circ \text{C}$ $3. \ 110^\circ \text{C}$ $4. \ 120^\circ \text{C}$

Options:

1. $102^\circ \text{C}$
2. $90^\circ \text{C}$
3. $110^\circ \text{C}$
4. $120^\circ \text{C}$

Solution:

$\text{Hint: } \frac{Q_1}{Q_2} = \frac{T_1}{T_2}$ $\text{Step: Find the temperature of the sink.}$ $\eta = 1 - \frac{Q_2}{Q_1} = 1 - \frac{T_2}{T_1}$ $\frac{Q_2}{Q_1} = \frac{T_2}{T_1}$ $\frac{225}{300} = \frac{T_2 + 273}{227 + 273}$ $\Rightarrow T_2 = 102^\circ \text{C}$

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
}