Two bars,A and B,each of length 2.0 m and cross sectional area 1.0 m²,are placed end to end as shown in the figure.
The thermal conductivities of the bars are
k A = 439 J/(s × m × K)and k B = 887 J/(s × m × K),respectively.The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K.
-How much heat passes the interface between A and B in 6.0 s?
A)6.0 × 10⁴ J
B)1.5 × 10³ J
C)1.2 × 10⁵ J
D)8.8 × 10⁴ J
E)3.0 × 10⁴ J

Question

Two bars,A and B,each of length 2.0 m and cross sectional area 1.0 m²,are placed end to end as shown in the figure.
 The thermal conductivities of the bars are
k A = 439 J/(s × m × K)and k B = 887 J/(s × m × K),respectively.The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K.
-How much heat passes the interface between A and B in 6.0 s?
A)6.0 × 10⁴ J 
B)1.5 × 10³ J 
C)1.2 × 10⁵ J 
D)8.8 × 10⁴ J 
E)3.0 × 10⁴ J

Quizplus · Accepted Answer

We can solve this problem by using the formula for heat transfer through a composite slab:

Q = (kAΔT)t / d

where Q is the heat transferred, k is the thermal conductivity, A is the area, ΔT is the temperature difference, t is the time, and d is the thickness.

In this case, we can treat the composite slab (bars A and B) as having a thickness of 2.0 m. The temperature difference across the slab is 100 K (373 K - 273 K). We can use the thermal conductivity of bar A since it is the first bar that heat passes through:

Q = (kAΔT)t / d
Q = (439 J/(s × m × K) × 1.0 m² × 100 K × 6.0 s) / 2.0 m
Q = 8.8 × 10⁴ J

Therefore, the answer is D) 8.8 × 10⁴ J.

Two Bars,A and B,each of Length 2