Import Question JSON

Current Question (ID: 11039)

Question:

$\text{During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of } C_P/C_V \text{ for the gas is equal to:}$

Options:

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

Solution:

$\text{As per the question:}$ $P \propto T^3$ $\text{As we know, } PV = nRT$ $\Rightarrow P \propto (PV)^3$ $\Rightarrow P^2V^3 = \text{constant}$ $\Rightarrow PV^{3/2} = \text{Constant}$ $\Rightarrow \gamma = \frac{3}{2} \Rightarrow \frac{C_P}{C_V} = \frac{3}{2}$

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
}