Heat and Thermodynamics 3 Question 16

16. Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0C and 90C respectively. The temperature of junction of the three rods will be

(2001,2M)

(a) 45C

(b) 60C

(c) 30C

(d) 20C

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Solution:

  1. Let θ be the temperature of the junction (say B ). Thermal resistance of all the three rods is equal. Rate of heat flow through AB+ Rate of heat flow through CB= Rate of heat flow through BD

90θR+90θR=θ0R

Here, R= Thermal resistance

3θ=180 or θ=60C

NOTE

Rate of heat flow

(H)= Temperature difference (TD) Thermal resistance (R) where, R=1KAK= Thermal conductivity of the rod. 

This is similar to the current flow through a resistance (R) where current (i) = Rate of flow of charge

= Potential difference (PD) Electrical resistance (R)

Here, R=lσA where σ= Electrical conductivity.



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