Import Question JSON

Current Question (ID: 11000)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): In an isothermal process, whole of the heat energy supplied to the body is converted into internal energy.}$ $\text{Reason (R): According to the first law of thermodynamics, } \Delta Q = \Delta U + \Delta W.$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{(A) is False but (R) is True.}$ (Correct)

Solution:

$\text{Hint: In an isothermal process, the temperature remains constant, so } \Delta U = 0.$ $\text{Explanation:}$ $\text{In an isothermal process, the temperature of the system remains constant throughout the process.}$ $\text{Since internal energy (U) is a function of temperature only for an ideal gas, when temperature is constant, } \Delta U = 0.$ $\text{According to the first law of thermodynamics: } \Delta Q = \Delta U + \Delta W$ $\text{For an isothermal process: } \Delta U = 0$ $\text{Therefore: } \Delta Q = 0 + \Delta W = \Delta W$ $\text{This means all the heat energy supplied to the system is converted into work done by the system, not internal energy.}$ $\text{Hence, Assertion (A) is False.}$ $\text{Reason (R) correctly states the first law of thermodynamics, so (R) is True.}$ $\text{Therefore, the correct answer is: (A) is False but (R) is True.}$

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
}