Match List-I with List-II. List-I: (A) Heat capacity of body (B) Specific heat capacity of body (C) Latent heat (D) Thermal conductivity List-II: (I) mathrmJkg^-1$\mathrm{Jkg^{-1}}$ (II) mathrmJK^-1$\mathrm{JK}^{-1}$ (III) mathrmJkg^-1K^-1$\mathrm{Jkg^{-1}K^{-1}}$ (IV) mathrmJm^-1mathrmK^-1mathrms^-1$\mathrm{Jm}^{-1}\mathrm{K}^{-1}\mathrm{s}^{-1}$ Choose the correct answer from the options given below:

### Related Formula Governing mathematical equations for thermal properties: 1. Heat capacity: C' = fracDelta QDelta T$C' = \frac{\Delta Q}{\Delta T}$ 2. Specific heat capacity: s = fracDelta Qm Delta T$s = \frac{\Delta Q}{m \Delta T}$ 3. Latent heat: L = fracDelta Qm$L = \frac{\Delta Q}{m}$ 4. Thermal conductivity: K = fracDelta Q cdot LA cdot Delta T cdot t$K = \frac{\Delta Q \cdot L}{A \cdot \Delta T \cdot t}$ ### Core Logic Let's derive the SI units for each property: - **(A) Heat capacity of body:** [C'] = fracmathrmJmathrmK = mathrmJK^-1 quad implies text(II)$$[C'] = \frac{\mathrm{J}}{\mathrm{K}} = \mathrm{JK^{-1}} \quad \implies \text{(II)}$$ - **(B) Specific heat capacity of body:** [s] = fracmathrmJmathrmkg cdot K = mathrmJkg^-1K^-1 quad implies text(III)$$[s] = \frac{\mathrm{J}}{\mathrm{kg \cdot K}} = \mathrm{Jkg^{-1}K^{-1}} \quad \implies \text{(III)}$$ - **(C) Latent heat:** [L] = fracmathrmJmathrmkg = mathrmJkg^-1 quad implies text(I)$$[L] = \frac{\mathrm{J}}{\mathrm{kg}} = \mathrm{Jkg^{-1}} \quad \implies \text{(I)}$$ - **(D) Thermal conductivity:** From heat transfer equation fracdQdt = K A fracdTdx$\frac{dQ}{dt} = K A \frac{dT}{dx}$: K = fracdQ/dtA (dT/dx) implies [K] = fracmathrmJ/smathrmm^2 cdot (mathrmK/m) = mathrmJ cdot m^-1 cdot K^-1 cdot s^-1 quad implies text(IV)$$K = \frac{dQ/dt}{A (dT/dx)} \implies [K] = \frac{\mathrm{J/s}}{\mathrm{m}^2 \cdot (\mathrm{K/m})} = \mathrm{J \cdot m^{-1} \cdot K^{-1} \cdot s^{-1}} \quad \implies \text{(IV)}$$ ### Step 1: Match values Applying our mappings: - (A) to$\to$ (II) - (B) to$\to$ (III) - (C) to$\to$ (I) - (D) to$\to$ (IV) This maps to Option (4). ### Pattern Recognition Sees: Dimensional unit matching of thermal parameters. Trap: Confusing Specific Heat Capacity (scaled per mass unit) with Heat Capacity (unscaled entire body parameter). Shortcut: Specific heat is normalized by mass, meaning its unit must contain kg in the denominator. Heat capacity has no mass constraint, meaning A maps directly to II. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Thermal Properties of Matter