Match List-I with List-II. List-I List-II (A) Thermal conductivity...

(A) Thermal conductivity ($K$): From the formula for heat conduction rate $\dfrac{dQ}{dt} = K A \dfrac{\Delta T}{\Delta x}$, the unit of $K$ is $\dfrac{\mathrm{W} \cdot \mathrm{m}}{\mathrm{m}^2 \cdot \mathrm{K}} = \mathrm{W}\ \mathrm{m}^{-1}\ \mathrm{K}^{-1}$.

(B) Specific heat capacity ($c$): From $Q = m c \Delta T$, the unit of $c$ is $\dfrac{\mathrm{J}}{\mathrm{kg} \cdot \mathrm{K}} = \mathrm{J}\ \mathrm{kg}^{-1}\ \mathrm{K}^{-1}$.

(C) Universal gas constant ($R$): From the ideal gas law $PV = nRT$, the unit of $R$ is $\dfrac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} = \mathrm{J}\ \mathrm{mol}^{-1}\ \mathrm{K}^{-1}$.

(D) Coefficient of linear expansion ($\alpha$): From $\Delta L = L \alpha \Delta T$, the unit of $\alpha$ is $\dfrac{\mathrm{m}}{\mathrm{m} \cdot \mathrm{K}} = \mathrm{K}^{-1}$.

Therefore, the correct matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).

Answer: (A)-(III), (B)-(IV), (C)-(I), (D)-(II)