In a composite slab, there are two materials | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In a steady state, the rate of heat flow $(H)$ through both slabs connected in series is the same.Let the temperature at the interface be $T$.The

Vedclass · Accepted Answer

$1/3$

Vedclass · Answer

(D) In a steady state, the rate of heat flow $(H)$ through both slabs connected in series is the same.Let the temperature at the interface be $T$.The rate of heat flow through the first slab is $H = \frac{KA(T_2 - T)}{x}$.The rate of heat flow through the second slab is $H = \frac{(2K)A(T - T_1)}{4x} = \frac{KA(T - T_1)}{2x}$.Equating the two expressions: $\frac{KA(T_2 - T)}{x} = \frac{KA(T - T_1)}{2x}$.This simplifies to $T_2 - T = \frac{T - T_1}{2}$, which gives $2T_2 - 2T = T - T_1$, or $3T = 2T_2 + T_1$, so $T = \frac{2T_2 + T_1}{3}$.Substituting $T$ back into the first equation: $H = \frac{KA}{x} \left( T_2 - \frac{2T_2 + T_1}{3} \right) = \frac{KA}{x} \left( \frac{3T_2 - 2T_2 - T_1}{3} \right) = \frac{KA(T_2 - T_1)}{3x}$.Comparing this with the given expression $\left[ \frac{A(T_2 - T_1)K}{x} \right] \cdot f$, we find $f = 1/3$.

Similar Questions

Two rods of the same length and material transfer a given amount of heat in $12 \ s$ when they are joined end to end. But when they are joined lengthwise parallel to each other,they will transfer the same amount of heat under the same conditions in a time of: (in $s$)

Consider the situation as shown in the figure. Find the amount of heat flowing per second through a cross-section of the bent part,if the total heat taken out per second from the end at $200^{\circ} C$ is $150 \ J/s$.

Two identical square rods of metal are welded end to end as shown in figure $(a)$. Assume that $10 \, cal$ of heat flows through the rods in $2 \, min$. Now the rods are welded as shown in figure $(b)$. The time it would take for $10 \, cal$ to flow through the rods now,is ........ $\min$.

Two walls have thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$,respectively. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. What is the temperature at the interface of the two walls?

Vedclass Test Series

Exam Paper Generator

Online Exam Module