Import Question JSON

Current Question (ID: 19671)

Question:

$\text{A sample of an ideal gas is taken through the cyclic process } abca \text{ as shown in the figure.}$ $\text{The change in the internal energy of the gas along the path } ca \text{ is } -180 \text{ J.}$ $\text{The gas absorbs } 250 \text{ J of heat along the path } ab \text{ and } 60 \text{ J along the path } bc.$ $\text{The work done by the gas along the path } abc \text{ is:}$

Options:

1. $140 \text{ J}$
2. $130 \text{ J}$
3. $100 \text{ J}$
4. $120 \text{ J}$

Solution:

$\Delta Q = \Delta U + \Delta W$ $\text{Given:}$ $\Delta U_{c \rightarrow a} = -180 \text{ J}, \Delta U_{a \rightarrow c} = +180 \text{ J (static function)}, \Delta Q_{a \rightarrow b} \rightarrow$ $\Delta Q = \Delta U + \Delta W$ $\Rightarrow \Delta Q_{a \rightarrow c} = \Delta U_{a \rightarrow c} + \Delta W_{a \rightarrow c}$ $\Rightarrow \Delta Q_{a \rightarrow b} + \Delta Q_{b \rightarrow c} = 180 + \Delta W_{a \rightarrow c}$ $250 + 60 = 180 + \Delta W_{a \rightarrow c}$ $\Rightarrow \Delta W_{a \rightarrow c} = 250 + 60 - 180$ $\Rightarrow \Delta W_{a \rightarrow c} = 130 \text{ J}$ $\text{Hence, option (2) is the correct answer.}$

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
}