Three rods of same dimensions have thermal conductivities k, 2 k, and 3 k . They are arranged as shown in figure with their ends at 100° C , 40° C and 0° C. The temperature of their junction is

Question

Three rods of same dimensions have thermal conductivities k, 2 k, and 3 k . They are arranged as shown in figure with their ends at 100° C , 40° C and 0° C. The temperature of their junction is (A) 40° C (B) 50° C (C) 60° C (D) 30° C

Tardigrade Admin · Accepted Answer

R1=(l/K A) R2=(l/2 K A) R3=(l/3 K A) R1: R2: R3:: 1: (1/2): (1/3) (d H1/d t)=(d H2/d t)+(d H3/d t) (100-T/R1)=(T-40/R2)+(T-0/R3) (100-T)=2(T-40)+3(T-0) 100-T=2 T-80+3 T 100+80=3 T+2 T+T T=30° C

Q. Three rods of same dimensions have thermal conductivities $k, 2 k$ , and $3 k .$ They are arranged as shown in figure with their ends at $10 0^{\circ} C, 4 0^{\circ} C$ and $0^{\circ} C$ . The temperature of their junction is

$4 0^{\circ} C$

$5 0^{\circ} C$

$6 0^{\circ} C$

$3 0^{\circ} C$

Q. Three rods of same dimensions have thermal conductivities k,2k, and 3k. They are arranged as shown in figure with their ends at 100∘C,40∘C and 0∘C. The temperature of their junction is

40∘C

50∘C

60∘C

30∘C

R1​=KAl​ R2​=2KAl​ R3​=3KAl​ R1​:R2​:R3​::1:21​:31​ dtdH1​​=dtdH2​​+dtdH3​​ R1​100−T​=R2​T−40​+R3​T−0​ (100−T)=2(T−40)+3(T−0) 100−T=2T−80+3T 100+80=3T+2T+T T=30∘C

Q. Three rods of same dimensions have thermal conductivities $k, 2 k$ , and $3 k .$ They are arranged as shown in figure with their ends at $10 0^{\circ} C, 4 0^{\circ} C$ and $0^{\circ} C$ . The temperature of their junction is

$4 0^{\circ} C$

$5 0^{\circ} C$

$6 0^{\circ} C$

$3 0^{\circ} C$