Import Question JSON

Current Question (ID: 11089)

Question:

$\text{Consider a cycle followed by an engine (figure).}$ $\text{1 to 2 is isothermal,}$ $\text{2 to 3 is adiabatic,}$ $\text{3 to 1 is adiabatic.}$ $\text{Such a process does not exist, because:}$

Options:

1. $\text{(a), (b)}$
2. $\text{(a), (c)}$ (Correct)
3. $\text{(b), (c)}$
4. $\text{(c), (d)}$

Solution:

$\text{Hint: Apply the concepts of the first and second laws of thermodynamics.}$ $\text{Step 1: Find the change in internal energy.}$ $\text{The given process is a cyclic process i.e. it returns to the original state 1.}$ $\text{Hence, the change in internal energy, } dU = 0.$ $\text{Step 2: Find the work done by the gas.}$ $\Rightarrow dQ = dU + dW = 0 + dW = dW$ $\text{Hence, the total heat supplied is converted to work done by the gas}$ $\text{(mechanical energy) which is not possible according to the second law of}$ $\text{thermodynamics.}$ $\text{Step 3: Find if all the processes are possible.}$ $\text{When the gas expands adiabatically from 2 to 3, it is not possible to return to}$ $\text{the same state without heat being supplied, hence, the process 3 to 1 cannot}$ $\text{be adiabatic.}$

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
}