Import Question JSON

Current Question (ID: 8290)

Question:

$\text{Select the correct option based on statements below:}$ $\begin{array}{|l|l|} \hline \text{Assertion (A):} & \text{Work done in an irreversible isothermal process at constant volume is zero.} \\ \hline \text{Reason (R):} & \text{Work is assigned a negative sign during expansion and is assigned a positive sign during compression.} \\ \hline \end{array}$

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. $\text{Both (A) and (R) are false.}$

Solution:

$\text{Hint: Work} = -P_{\text{ext}}\Delta V$ $\text{Analysis of Assertion (A):}$ $\text{For a thermodynamic process, the mechanical work done by a system can be expressed as:}$ $W = -P_{\text{ext}}\Delta V$ $\text{where } P_{\text{ext}} \text{ is the external pressure and } \Delta V \text{ is the change in volume.}$ $\text{In a constant volume process (isochoric process), } \Delta V = 0 \text{, regardless of whether the process is reversible or irreversible, isothermal or non-isothermal.}$ $\text{Therefore, } W = -P_{\text{ext}} \times 0 = 0$ $\text{Hence, the work done in any constant volume process, including an irreversible isothermal process at constant volume, is zero.}$ $\text{Assertion (A) is true.}$ $\text{Analysis of Reason (R):}$ $\text{The formula for work done by a system in terms of pressure and volume change is:}$ $W = -P(V_2 - V_1)$ $\text{In the case of expansion, } V_2 > V_1 \text{, which makes } (V_2 - V_1) \text{ positive. Therefore, } W = -P \times \text{(positive value)} \text{, making work negative during expansion.}$ $\text{In the case of compression, } V_2 < V_1 \text{, which makes } (V_2 - V_1) \text{ negative. Therefore, } W = -P \times \text{(negative value)} \text{, making work positive during compression.}$ $\text{This aligns with the convention that work done by the system on the surroundings (expansion) is negative, and work done on the system by the surroundings (compression) is positive.}$ $\text{Reason (R) is true.}$ $\text{Relationship between (A) and (R):}$ $\text{While both statements are true, the reason (R) does not explain why work done in a constant volume process is zero. The reason for work being zero in a constant volume process is that } \Delta V = 0 \text{, not because of the sign conventions for expansion and compression work.}$ $\text{The sign convention for work is a general principle in thermodynamics and does not specifically explain the zero work in constant volume processes.}$ $\text{Therefore, both (A) and (R) are true, but (R) is not the correct explanation of (A).}$

Import JSON File

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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
}