Import Question JSON

Current Question (ID: 11056)

Question:

$\text{If a gas undergoes the change in its thermodynamic state from A to B via two different paths, as shown in the given pressure (P) versus volume (V) graph, then:}$

Options:

1. $\text{the temperature of the gas decreases in path 1 from A to B.}$
2. $\text{the heat absorbed by the gas in path 1 is greater than in path 2.}$ (Correct)
3. $\text{the heat absorbed by the gas in path 2 is greater than in path 1.}$
4. $\text{the change in internal energy in path 1 is greater than in path 2.}$

Solution:

$\text{Hint: Find the work done for paths.}$ $\text{Step 1: Find temperature change in path 1.}$ $\text{Since both paths connect the same initial state A and final state B, the change in internal energy } \Delta U \text{ is the same for both paths (internal energy is a state function).}$ $\text{Step 2: Compare the work done in both paths.}$ $\text{Work done = area under P-V curve}$ $\text{Path 1 (curved path): Larger area under curve } \Rightarrow W_1 > W_2$ $\text{Path 2 (straight line): Smaller area under curve}$ $\text{Step 3: Find the change in internal energy for both paths.}$ $\text{From first law: } \Delta U = \Delta Q - W$ $\text{Since } \Delta U \text{ is same for both paths:}$ $\Delta Q_1 - W_1 = \Delta Q_2 - W_2$ $\text{Rearranging: } \Delta Q_1 - \Delta Q_2 = W_1 - W_2$ $\text{Since } W_1 > W_2\text{, we have } \Delta Q_1 > \Delta Q_2$ $\text{Therefore, the heat absorbed by the gas in path 1 is greater than in path 2.}$

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
}