Import Question JSON

Current Question (ID: 11160)

Question:

$\text{One mole of an ideal diatomic gas undergoes a transition from } A \text{ to } B \text{ along a path } AB \text{ as shown in the figure.}$ $\text{The change in internal energy of the gas during the transition is:}$

Options:

1. $20 \text{ kJ}$
2. $-20 \text{ kJ}$ (Correct)
3. $20 \text{ J}$
4. $-12 \text{ kJ}$

Solution:

$\text{Hint: The internal energy depends only on the temperature of a gas.}$ $\text{Step 1: Find the } C_V \text{ of the gas.}$ $C_V = \frac{R}{\gamma-1} = \frac{5R}{2}$ $\text{Step 2: Find the change in product } PV$ $\Delta(PV) = P_2V_2 - P_1V_1 = -8\text{kPam}^3$ $\Rightarrow \Delta(PV) = -8 \text{ kJ} = nR\Delta T$ $\text{Step 3: Find the change in the internal energy of the gas.}$ $\text{Use the formula for the change in the internal energy:}$ $\Delta U = nC_V\Delta T$ $\Delta U = \frac{5}{2}[nR\Delta T]$ $\Rightarrow \Delta U = -20 \text{ kJ}$ $\text{Hence, option (2) is the correct answer.}$

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
}