Question

Q=KA(T1-T2)t/L in K=thermal conductivity of the material rod, A=area of cross sectional T1 and T2 are temperature of hot and cold ends, respectively t=time and L=lenth .obtain dimensional formula of K

Answer 1

Q=KA(T1-T2)t/L now k=cofficent of thermal conductivity. k it's dimension MLT-1K-1(k is dimension of temperature in kelvin.

Answer 2

Answer:

• The dimensional formula of the thermal conductivity (K) can be obtained by analyzing the dimensions of each term in the equation Q=KA(T1-T2)t/L.
• First, the heat transfer rate (Q) has dimensions of energy/time, or [Q] = [M][L^2][T^-2].
• Next, the thermal conductivity (K) has dimensions of energy/length/temperature, or [K] = [M][L^-1][T^-2].
• The area of cross section (A) has dimensions of length^2, or [A] = [L^2].
• The temperature difference (T1-T2) has dimensions of temperature, or [T1-T2] = [T].
• The time (t) has dimensions of time, or [t] = [T].
• Finally, the length (L) has dimensions of length, or [L] = [L].
• Equating the dimensions on both sides of the equation, we can see that [Q] = [K][A][(T1-T2)][t]/[L]. Thus, [K] = [Q][L]/[A][(T1-T2)][t], giving us the dimensional formula of the thermal conductivity.
• In conclusion, the dimensional formula of thermal conductivity (K) is [K] = [M][L^-1][T^-2].

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