Import Question JSON

Current Question (ID: 11170)

Question:

$\text{The figure shows a process for a gas in which pressure (P) and volume (V) of the gas change. If } C_1 \text{ and } C_2 \text{ are the molar heat capacities of the gas during the processes AB and BC respectively, then:}$

Options:

1. $C_1 = C_2$
2. $C_1 > C_2$
3. $C_1 < C_2$ (Correct)
4. $C_1 \leq C_2$

Solution:

$\text{Hint: Use } C_p - C_v = R.$ $\text{Step 1: Identify the processes}$ $\text{AB - Isochoric}$ $\text{BC - Isobaric}$ $\text{Step 2: Find the molar specific heats } C_1 \text{ and } C_2$ $C_1 = C_v$ $C_2 = C_p$ $C_p - C_v = R$ $\Rightarrow C_p = C_v + R$ $\Rightarrow C_p > C_v$ $\text{Hence, } C_2 > C_1$

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
}