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Current Question (ID: 19701)

Question:

$\text{Match Column-I with Column-II and select the correct option.}$ $\begin{array}{|c|c|} \hline \text{Column-I} & \text{Column-II} \\ \hline \text{P. Adiabatic process} & \text{A. no work done by or on gas} \\ \text{Q. Isochoric process} & \text{B. some amount of heat given is converted into internal energy} \\ \text{R. Isobaric process} & \text{C. no heat exchange} \\ \text{S. Isothermal process} & \text{D. no change in internal energy} \\ \hline \end{array}$

Options:

1. $\text{P} \rightarrow \text{A}, \text{Q} \rightarrow \text{B}, \text{R} \rightarrow \text{C}, \text{S} \rightarrow \text{D}$
2. $\text{P} \rightarrow \text{A}, \text{Q} \rightarrow \text{C}, \text{R} \rightarrow \text{D}, \text{S} \rightarrow \text{B}$
3. $\text{P} \rightarrow \text{C}, \text{Q} \rightarrow \text{A}, \text{R} \rightarrow \text{B}, \text{S} \rightarrow \text{D}$
4. $\text{P} \rightarrow \text{B}, \text{Q} \rightarrow \text{D}, \text{R} \rightarrow \text{C}, \text{S} \rightarrow \text{A}$

Solution:

$\text{Hint: Recall the thermodynamic processes.}$ $\text{Explanation: In an adiabatic process, the system is insulated from the surroundings, and heat absorbed or released is zero i.e., no heat exchange. Therefore, P} \rightarrow \text{C.}$ $\text{In isochoric processes, the volume is constant i.e., } \Delta V = 0. \text{ So, work done by or on the gas } W = P \Delta V = 0. \text{ Therefore, Q} \rightarrow \text{A.}$ $\text{In isobaric processes, the pressure is constant i.e., } \Delta P = 0. \text{ So, some amount of heat given is converted into internal energy. Therefore, R} \rightarrow \text{B.}$ $\text{A process in which the temperature of the system is kept fixed throughout is called an isothermal process i.e., } \Delta T = 0. \text{ So, there is no change in internal energy. Therefore, S} \rightarrow \text{D.}$ $\text{Therefore, the correct match is P} \rightarrow \text{C; Q} \rightarrow \text{A; R} \rightarrow \text{B; S} \rightarrow \text{D.}$ $\text{Hence, option (3) is the correct answer.}$

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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
}