Import Question JSON

Current Question (ID: 11047)

Question:

$\text{Two cylinders, } A \text{ and } B\text{, of equal capacity are connected to each other via a stopcock. } A \text{ contains gas at a standard temperature and pressure } B \text{ is completely evacuated. The entire system is thermally insulated. If the stopcock is suddenly opened, then the change in internal energy of the gas is:}$

Options:

1. $0$ (Correct)
2. $5 \text{ J}$
3. $1 \text{ J}$
4. $3 \text{ J}$

Solution:

$\text{Hint: } W = \Delta Q + \Delta U$ $\text{Step: Find the change in the internal energy of the gas.}$ $\text{The work done by the gas in chamber } A \text{ is zero as chamber } B \text{ is a vacuum(having zero pressure). The work is only done if there is external pressure.}$ $\Rightarrow W = 0$ $\text{As the entire system is thermally insulated so;}$ $\Rightarrow Q = 0$ $\text{Using the first law of thermodynamics we get;}$ $W = \Delta Q + \Delta U$ $\text{Substitute the known values we get;}$ $\Rightarrow \Delta U = 0$ $\text{Hence, option (1) is the correct answer.}$

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
}