Question 22: Thermodynamics & KTG

Question

Two rods $P$ and $Q$ have equal lengths. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$. When the temperature at ends of each rod are $T_1$ and $T_2$ respectively, the rate of flow of heat through $P$ and $Q$ will be equal, if

Accepted Answer

$$ \begin{aligned} & 	ext { As, }\left(\frac{\Delta Q}{\Delta t}ight)_P=\left(\frac{\Delta Q}{\Delta t}ight)_Q \ & \Rightarrow K_1 A_1 \frac{\left(T_1-T_2ight)}{l}=K_2 A_2 \frac{\left(T_1-T_2ight)}{l} \ & 	ext { or } \quad K_1 A_1=K_2 A_2 	ext { or } \frac{A_1}{A_2}=\frac{K_2}{K_1} \end{aligned} $$

Answer

$\frac{A_1}{A_2}=\frac{K_2}{K_1}$

Answer

$\frac{A_1}{A_2}=\frac{K_2}{K_1} 	imes \frac{T_2}{T_1}$

Answer

$\frac{A_1}{A_2}=\sqrt{\frac{K_1}{K_2}}$

Answer

$\frac{A_1}{A_2}=\left(\frac{K_2}{K_1}\right)^2$

Thermodynamics & KTG

Two rods P and Q have equal lengths. Their thermal conductivities are K_1 and K_2 and cross-sectional areas are A_1 and A_2. When the temperature at ends of each rod are T_1 and T_2 respectively, the rate of flow of heat through P and Q will be equal, if

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