Import Question JSON

Current Question (ID: 19725)

Question:

$\text{A certain amount of gas of volume } V \text{ at } 27^\circ C \text{ temperature and}$ $\text{pressure } 2 \times 10^7 \text{ Nm}^{-2} \text{ expands isothermally until its volume gets}$ $\text{doubled. Later, it expands adiabatically until its volume gets}$ $\text{redoubled. The final pressure of the gas will be: (Use } \gamma = 1.5)$

Options:

1. $3.536 \times 10^5 \text{ Pa}$
2. $3.536 \times 10^6 \text{ Pa}$
3. $1.25 \times 10^6 \text{ Pa}$
4. $1.25 \times 10^5 \text{ Pa}$

Solution:

$\text{Hint: } P_1V_1 = P_2V_2$ $\text{Step 1: Find the pressure of the gas after the isothermal}$ $\text{expansion.}$ $PV = P'(2V)$ $P' = \frac{P}{2}$ $\text{Step 2: Find the final pressure of the gas.}$ $P_2(V_2)^\gamma = P_3(2V_2)^\gamma$ $P_3 = \frac{1 \times 10^7}{2^{1.5}} = 3.536 \times 10^6 \text{ Pa}$ $\text{Hence, option (2) is the correct answer.}$

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
}