Two identical bars are conducting heat from a region of higher temperature to one of lower temperature. In arrangement A, the bars conduct 80 J of heat in a certain amount of time. How much heat is conducted in B during the same time

Q' = 320 J

Explanation:

The arrangements are given in attachment. The Fourier's Law of Heat Conduction states that:

Q = KAΔT/L

where,

Q = Heat Transferred

K = Constant (Conduction Coefficient)

A = Surface Area of Heat Transfer

ΔT = Difference of Temperature between two surfaces

L = Length between surfaces

For Arrangement AL

Q = 80 J

Therefore,

80 = KAΔT/L   ------------- equation (1)

Now, for arrangement B:

A' = 2 A (As, the rods are now connected in parallel with each other)

L' = L/2

Therefore,

Q' = K(2A)ΔT/(L/2)

Q' = 4 KAΔT/L

using equation (1)

Q' = 4(80 J)

Q' = 320 J

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day