Import Question JSON

Current Question (ID: 11162)

Question:

$\text{The pressure in a diatomic gas increases from } P_0 \text{ to } 3P_0\text{, when its volume is increased from } V_0 \text{ to } 2V_0\text{. The increase in internal energy will be:}$

Options:

1. $6P_0 V_0$
2. $8.5P_0 V_0$
3. $12.5P_0 V_0$ (Correct)
4. $14.5P_0 V_0$

Solution:

$\text{Hint: Internal energy depends only on temperature.}$ $\text{Step 1: From the graph, find the change in the product (PV).}$ $PV = nRT$ $P_1 V_1 = nRT_1$ $P_2 V_2 = nRT_2$ $P_2 V_2 - P_1 V_1 = nR \Delta T = 5P_0 V_0$ $\text{Step 2: Calculate } C_V\text{.}$ $C_V = \frac{R}{\gamma - 1} = \frac{R}{\frac{7}{5} - 1} = \frac{5R}{2}$ $\text{Step 3: Calculate } \Delta U\text{.}$ $\Delta U = nC_V \Delta T$ $= \frac{5}{2} nR \Delta T$ $= 12.5 P_0 V_0$

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
}