Match the following columns,
`{:("Column1","Column2"),("a Thermal resitance","p [MT^(-3)K^(-4)]"),("b Stefan's constant","q [M^(-1)L^(-2)T^(3)K]"),("c Wien's constant","r [ML^(2)T^(-3)]"),("d Heat current","s [LK]"):}`

Answer

To solve the problem of matching the physical quantities in Column 1 with their respective dimensions in Column 2, we will analyze each quantity step by step.

### Step-by-Step Solution:

1. **Thermal Resistance (A)**:
- The unit of thermal resistance is Kelvin per watt (K/W).
- Power (watt) can be expressed as work done per unit time, which has the dimension of \(ML^2T^{-3}\).
- Therefore, the dimension of thermal resistance can be calculated as:
\[ \text{Thermal Resistance} = \frac{K}{\text{Power}} = \frac{K}{ML^2T^{-3}} = M^{-1}L^{-2}T^3K \]
- This matches with \(q [M^{-1}L^{-2}T^3K]\).
- **Match**: A → q

2. **Stefan's Constant (B)**:
- The unit of Stefan's constant is watts per square meter per Kelvin to the fourth power (W/m²K⁴).
- Substituting the dimension of power:
\[ \text{Stefan's Constant} = \frac{ML^2T^{-3}}{L^2K^4} = M L^0 T^{-3} K^{-4} \]
- This simplifies to \(M T^{-3} K^{-4}\).
- **Match**: B → p [M^(-1)L^(-2)T^(3)K]

3. **Wien's Constant (C)**:
- Wien's displacement law relates wavelength (λ) and temperature (T). The dimension of wavelength is length (L), and temperature is in Kelvin (K).
- Therefore, the dimension of Wien's constant is:
\[ \text{Wien's Constant} = L K \]
- **Match**: C → s [LK]

4. **Heat Current (D)**:
- Heat current (H) can be expressed as the change in temperature (ΔT) divided by thermal resistance (Rth).
- The dimension of ΔT is K, and we already calculated the dimension of thermal resistance as \(M^{-1}L^{-2}T^3K\).
- Therefore, the dimension of heat current is:
\[ \text{Heat Current} = \frac{K}{M^{-1}L^{-2}T^3K} = M L^2 T^{-3} \]
- **Match**: D → r [ML^(2)T^(-3)]

### Final Matches:
- A → q
- B → p
- C → s
- D → r