Question

Match the quantities in Group 1 with their units in Group 2

Group 1	Group 2
P) Thermal conductivity	I) \( \text{W·m}^{-2}\text{K}^{-1} \)
Q) Convective heat transfer coefficient	II) \( \text{W·m}^{-1}\text{K}^{-1} \)
R) Stefan-Boltzmann constant	III) \( \text{W·K}^{-1} \)
S) Heat capacity rate	IV) \( \text{W·m}^{-2}\text{K}^{-4} \)

• A. P-II, Q-I, R-IV, S-III
• B. P-I, Q-II, R-III, S-IV
• C. P-III, Q-IV, R-II, S-I
• D. P-IV, Q-I, R-III, S-II

Hint:

- Always recall standard 64ac0493b52af67589bd410c units: • \(k\) (thermal conductivity) → W·m\(^{-1}\)K\(^{-1}\)
• \(h\) (convective coefficient) → W·m\(^{-2}\)K\(^{-1}\)
• \(\sigma\) (Stefan–Boltzmann constant) → W·m\(^{-2}\)K\(^{-4}\)
• Heat capacity rate → W·K\(^{-1}\)

Answer 1

The Correct Option is A

Step 1: Units of thermal conductivity. \[ k: \;\; \frac{\text{W}}{\text{mK}} = \text{Wm}^{-1}\text{K}^{-1}. \] So, \( P \;\rightarrow\; II \). 

Step 2: Units of convective heat transfer coefficient. Defined as: \[ q = hA\Delta T. \] Hence, \[ h: \;\; \frac{\text{W}}{\text{m}^2 \text{K}} = \text{Wm}^{-2}\text{K}^{-1}. \] So, \( Q \;\rightarrow\; I \).

Step 3: Units of Stefan–Boltzmann constant. From: \[ q = \sigma T^4, \] we get: \[ \sigma: \;\; \frac{\text{W}}{\text{m}^2 \text{K}^4} = \text{Wm}^{-2}\text{K}^{-4}. \] So, \( R \;\rightarrow\; IV \).

Step 4: Units of heat capacity rate. Defined as: \[ C = \dot m c_p, \] which has units: \[ \frac{\text{J}}{\text{Ks}} = \text{WK}^{-1}. \] So, \( S \;\rightarrow\; III \).

Correct Matching: \[ \boxed{ P \;\rightarrow\; II, \quad Q \;\rightarrow\; I, \quad R \;\rightarrow\; IV, \quad S \;\rightarrow\; III } \] Option (A)