Question

The character Wolverine has had his bones replaced with a high-density, high-strength metal alloy called Adamantium, which has the following properties:

A density of 8 g/cm³

A specific heat of 0.462 kJ/kg K, and

A coefficient of linear expansion of 14 x 10^-6/C°.

During a certain fight, Wolverine's core body temperature increases from 38C to 40C. Now let's model one of his femur bones (thigh) as a cylinder with a radius of 1.25 cm and a length of 52 cm.

(Note: Double check your units on the questions that follow. What is the mass of one of his humerus bones?

m = ?

How much energy did the bone have to absorb in order for its temperature to have increased?

Q = ?

By how much does the length of his bone increase?

ΔL = ?

Answer 1

length = 52 cm

radius = 1.25 cm

volume = 2pi*r*l =408.407 cm³

now, density = 8 g/cm³

so, mass = 408.407 cm³* 8 = 3267.25 g = 3.267 Kg

Q = m*Sp * dT

where , sp is the specific heat

dT is the temperature rise

=3.267kg * 0.462 kJ/kg K * (40-38)

=3.018 KJ of energy is absorbed

for linear expansion,

where/L is the change in length in metres -1 α is the coefficient of linear expansion in °C L is the original length, in metres T is the temperature change in °C

so increase in length

=14 x 10^-6/C°.* 0.52 m *(40-38)

= 1.456 x10^-5 m increase in length of bone

=14.56 micrometer increase