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Current Question (ID: 11083)

Question:

$\text{If in the thermodynamic process shown in the figure, the work done by the}$ $\text{system along } A \rightarrow B \rightarrow C \text{ is 50 J and the change in internal energy during } C$ $\rightarrow A \text{ is 30 J, then the heat supplied during } A \rightarrow B \rightarrow C \text{ is:}$

Options:

1. $50 \text{ J}$
2. $20 \text{ J}$ (Correct)
3. $10 \text{ J}$
4. $80 \text{ J}$

Solution:

$\text{Hint: Internal energy depends on the initial and final stages.}$ $\text{Step 1: Use the 1st law of thermodynamics to calculate heat supplied during}$ $A \rightarrow B \rightarrow C.$ $\text{given that}$ $W_{A \rightarrow B \rightarrow C} = 50 \text{ J}$ $U_{C \rightarrow A} = 30 \text{ J}$ $\Delta U_{A \rightarrow C} = -U_{C \rightarrow A} = -30 \text{ J}$ $\text{Step 2: use 1st law of thermodynamics.}$ $\Delta Q = \Delta U + \Delta W$ $= -30 + 50$ $= 20 \text{ J}.$

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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
}