Import Question JSON

Current Question (ID: 11072)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): It is possible that the temperature of a gas may fall even as it is being heated.}$ $\text{Reason (R): The specific heat capacity of a gas changes from process to process.}$

Options:

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

Solution:

$\text{Hint: Recall the first law of thermodynamics.}$ $\text{Analysis of Assertion (A):}$ $\text{According to the first law of thermodynamics: } \Delta U = Q - W$ $\text{where } \Delta U \text{ is change in internal energy, } Q \text{ is heat added, and } W \text{ is work done by the system.}$ $\text{For an ideal gas, internal energy depends only on temperature: } \Delta U = nC_V\Delta T$ $\text{If heat is being added (Q > 0) but the gas expands and does significant work (W > Q), then } \Delta U < 0$ $\text{This means } \Delta T < 0, \text{ so temperature can decrease even when heat is added.}$ $\text{Therefore, Assertion (A) is True.}$ $\text{Analysis of Reason (R):}$ $\text{The specific heat capacity of a gas does indeed change from process to process.}$ $\text{For example: } C_P \text{ (constant pressure), } C_V \text{ (constant volume), and different values for other processes.}$ $\text{Therefore, Reason (R) is also True.}$ $\text{However, (R) does not correctly explain (A). The temperature drop during heating is due to work done by the gas during expansion, not because specific heat capacity changes.}$ $\text{The correct answer is option 2: Both (A) and (R) are True but (R) is not the correct explanation of (A).}$

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
}