Question

Four rods each of the same initial length but made of copper, glass, iron and aluminium are heated to the same rise in temperature. Which rod will expand more?

Answer 1

This question can be answered using the concept of specific heat. Specific heat can be defined as the amount of heat required to raise the temperature of a body i.e. exactly one gram by one degree.
Heat capacity is the amount of heat required to change the heat content of one mole of material by one degree.
We are given four rods of the same initial length but made of copper, glass, iron and aluminium are heated to the same rise in temperature. The rod having the highest specific heat will absorb the maximum amount of heat and it will expand the most.

Complete step by step solution:
The specific heat of the four rods are,
Specific heat of Copper: $0.385{J \mathord{\left/ {\vphantom {J {{g^ \circ }}}} \right.} {{g^ \circ }}}C$
Specific heat of Aluminium: $0.902{J \mathord{\left/ {\vphantom {J {{g^ \circ }}}} \right.} {{g^ \circ }}}C$
Specific heat of iron: $0.450{J \mathord{\left/ {\vphantom {J {{g^ \circ }}}} \right.} {{g^ \circ }}}C$
Specific heat of glass: $0.84{J \mathord{\left/ {\vphantom {J {{g^ \circ }}}} \right.} {{g^ \circ }}}C$
We know that,
$Q = mc\Delta t$
Where Q is the quantity of heat absorbed.
M is the mass of the body.
C is the specific heat.
$\Delta t$ is the change in temperature.
So specific heat is highest for aluminium Q will be highest for aluminium and thus the heat absorbed. So it will expand maximum.

Additional Information:
Specific heat can be determined in the following ways. When two materials of different temperatures are brought to contact then heat flows from warmer substance to colder substance until both the temperatures are equal. Heat gained by the colder material must be equal to heat lost by the warmer material.

Note:
Specific heat capacity of water is higher than most of the materials because of the presence of hydrogen bonds. Due to the presence of hydrogen bonds higher energy is needed to break those bonds. Water absorbs heat without immediate rise in temperature and can retain it for longer time. This property of water is used to maintain our body temperature.