Question

One end of a 0.25 m long metal bar is in steam and the other is in contact with ice . If 12 g of ice melts per minute, what is the thermal conductivity of the metal? Given cross-section of the bar =5×10⁻⁴m² and latent heat of ice is 80calg⁻¹

A. 20cals⁻¹m⁻¹.∘C⁻¹
B. 10cals⁻¹m⁻¹.∘C⁻¹
C. 40cals⁻¹m⁻¹.∘C⁻¹
D. 80cals⁻¹m⁻¹.∘C⁻¹

Answer 1

The thermal conductivity of the metal is determined as 80 cals⁻¹m⁻¹.∘C⁻¹. (Option D).

How to calculate the thermal conductivity of the metal?

The thermal conductivity of the metal is calculated as follows.

Q = (k × A × Δθ × t ) / d

where;

• Q is the heat transferred
• k is the thermal conductivity of the material
• A is the cross-sectional area through which heat is conducted
• Δθ is the temperature difference across the bar
• t is the time of heat transfer
• d is the length of the bar

k = Qd / (A × Δθ × t)

The heat transferred is calculated as;

Q = mass x latent heat of ice

Q = 12 g x 80 cal/g

Q = 960 cal

The thermal conductivity of the metal is calculated as;

k = Qd / (A × Δθ × t)

Δθ = (100⁰C - 0⁰C) = 100⁰C

t = 1 min x 60 s = 60 s

k = (960 x 0.25) / (5 x 10⁻⁴ x 100 x 60 )

k = 80 cals⁻¹m⁻¹.∘C⁻¹