Import Question JSON

Current Question (ID: 8250)

Question:

$\text{When a gas undergoes adiabatic expansion, it gets cooled due to -}$

Options:

1. $\text{Loss of energy}$
2. $\text{Fall in pressure}$
3. $\text{Decrease in velocity}$
4. $\text{Increase in energy with work done}$

Solution:

\textbf{Hint: } \text{Adiabatic process, } dq = 0 \Delta U = \Delta q + W \text{When adiabatic expansion takes place, then:} \Delta q = 0, \text{ W is negative} W < 0, \text{ therefore } W = \Delta U \Delta U < 0 \text{In an adiabatic process, there is no heat exchange with the surroundings } (dq = 0). \text{ During adiabatic expansion:} \text{• The gas does work on the surroundings, so work done by the gas is positive, but work done on the gas is negative } (W < 0) \text{• From the first law of thermodynamics: } \Delta U = q + W \text{• Since } q = 0 \text{ and } W < 0, \text{ therefore } \Delta U < 0 \text{• A decrease in internal energy } (\Delta U < 0) \text{ corresponds to a decrease in temperature, causing the gas to cool} \text{The cooling occurs because the gas loses internal energy (and hence temperature) as it does work during expansion, with no compensating heat input from the surroundings.} \text{Hence, the first option 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
}