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Current Question (ID: 21023)

Question:

$\text{Which one of the following equations does not correctly represent the}$ $\text{first law of thermodynamics for the given processes involving an}$ $\text{ideal gas? (Assume non-expansion work is zero)}$ $1.\ \text{Adiabatic process: } \Delta U = -w$ $2.\ \text{Cyclic process: } q = -w$ $3.\ \text{Isothermal process: } q = -w$ $4.\ \text{Isochoric process: } \Delta U = q$

Options:

1. $\Delta U = -w$
2. $q = -w$
3. $q = -w$
4. $\Delta U = q$

Solution:

$\text{Hint: For adiabatic process, } q \text{ is zero.}$ $\text{1st law of thermodynamics}$ $\Delta E = q + w$ $1.\ \text{Adiabatic process}$ $q = 0,\ (\Delta E = w)\ \text{or}\ (\Delta U = w)$ $2.\ \text{Cyclic process}$ $\Delta E = 0\ \text{or}\ (q = -w)$ $3.\ \text{Isothermal process}$ $\Delta E = nC_V \Delta T,\ (\Delta T = 0)$ $\Delta E = 0,\ (q = -w)$ $4.\ \text{Isochoric process } \Delta V = 0$ $w = -P \Delta V = 0$ $\Delta E = q$

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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
}