Import Question JSON

Current Question (ID: 11038)

Question:

$\text{The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state A to state B will be:}$

Options:

1. $\frac{2}{5}$ (Correct)
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{2}{7}$

Solution:

$\text{Hint: The given process is an isobaric process.}$ $\text{Step: Find the ratio of work done by the gas to the heat absorbed by it.}$ $\text{It is clearly seen from the graph, that the volume is directly proportional to the temperature, therefore the given process is the isobaric process.}$ $\frac{W}{Q} = \frac{nR\Delta T}{nC_P\Delta T}$ $\frac{W}{Q} = \frac{R}{C_P} \Rightarrow \frac{R}{5R/2}$ $\Rightarrow \frac{W}{Q} = \frac{2}{5}$ $\text{Hence, option (1) is the correct answer.}$

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
}