Two plates of equal area are placed in contac | vedclass

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

Question

(A) Let the thickness of the first plate be $x_1 = 2$ and the second plate be $x_2 = 3$. Let the temperature of the contact surface be $	heta$. The h

Vedclass · Accepted Answer

$(a) -5^{\circ}C, (b) 0^{\circ}C$

Vedclass · Answer

(A) Let the thickness of the first plate be $x_1 = 2$ and the second plate be $x_2 = 3$. Let the temperature of the contact surface be $	heta$. The heat flow rate through both plates in series must be equal: $\frac{dQ}{dt} = \frac{K_1 A (T_1 - 	heta)}{x_1} = \frac{K_2 A (	heta - T_2)}{x_2}$.$(a)$ If they are of the same material,$K_1 = K_2 = K$. Given $T_1 = -25^{\circ}C$ and $T_2 = 25^{\circ}C$ (or vice versa,the setup implies a gradient between $-25^{\circ}C$ and $25^{\circ}C$). Using the steady state condition: $\frac{K A (	heta - (-25))}{2} = \frac{K A (25 - 	heta)}{3}$.$3(	heta + 25) = 2(25 - 	heta) \Rightarrow 3	heta + 75 = 50 - 2	heta \Rightarrow 5	heta = -25 \Rightarrow 	heta = -5^{\circ}C$.$(b)$ If thermal conductivities are in ratio $K_1 : K_2 = 2 : 3$,then $\frac{2 A (	heta + 25)}{2} = \frac{3 A (25 - 	heta)}{3}$.$	heta + 25 = 25 - 	heta \Rightarrow 2	heta = 0 \Rightarrow 	heta = 0^{\circ}C$.

Similar Questions

Two ends of rods of length $L$ and radius $r$ of the same material are kept at the same temperature difference. Which of the following rods conducts the most heat?

The coefficients of thermal conductivity of copper,mercury,and glass are respectively $K_c, K_m$,and $K_g$ such that $K_c > K_m > K_g$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_c, X_m$,and $X_g$,then:

Three rods made of the same material and having the same cross-sectional area but different lengths $10 \ cm$,$20 \ cm$,and $30 \ cm$ are joined as shown. The temperature of the joint is ....... $^oC$.

Two different rods $A$ and $B$ are kept in series as shown in the figure. The variation of temperature across different cross-sections is plotted in the graph. The ratio of thermal conductivities of $A$ and $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module