Know that a rise in the temperature of an object increases its internal energy

2.2.2 Specific Heat Capacity

Learning Objective

Understand that a rise in the temperature of an object increases its internal energy and be able to use the relationship between heat energy, mass, specific heat capacity and temperature change.

Key Concepts

• Internal energy (U): the total kinetic energy of the particles in a substance.
• Temperature (T): a measure of the average kinetic energy of the particles.
• Specific heat capacity (c): the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K). Units: \$J\,kg^{-1}\,K^{-1}\$.
• Heat energy (Q): the energy transferred because of a temperature difference. Units: \$J\$.

Fundamental Relationship

The quantitative link between heat energy, mass, specific heat capacity and temperature change is given by:

\$Q = mc\Delta T\$

where

• \$Q\$ = heat energy added to or removed from the object (\$J\$)
• \$m\$ = mass of the object (\$kg\$)
• \$c\$ = specific heat capacity of the material (\$J\,kg^{-1}\,K^{-1}\$)
• \$\Delta T = T{\text{final}} - T{\text{initial}}\$ = change in temperature (\$K\$ or \$°C\$)

Why a Rise in Temperature Increases Internal Energy

When heat \$Q\$ is supplied to a substance, its particles move faster, increasing their kinetic energy. Since internal energy \$U\$ is the sum of the kinetic energies of all particles, \$U\$ rises proportionally to the temperature increase.

Typical Specific Heat Capacities

Worked Example

1. Calculate the heat energy required to raise 250 g of water from \$20\,°C\$ to \$80\,°C\$.
2. Given: \$c_{\text{water}} = 4180\;J\,kg^{-1}\,K^{-1}\$.

Solution:

Convert mass to kilograms: \$m = 250\;g = 0.250\;kg\$.

Temperature change: \$\Delta T = 80 - 20 = 60\;K\$.

Apply the formula:

\$Q = (0.250\;kg)(4180\;J\,kg^{-1}\,K^{-1})(60\;K) = 62\,700\;J\$

Therefore, \$62.7\;kJ\$ of heat must be supplied.

Implications for Everyday Situations

• Heating water on a stove requires more energy than heating the same mass of oil because water has a higher \$c\$.
• Metal cookware heats up quickly (low \$c\$) but also cools quickly, whereas a ceramic pot retains heat longer (higher \$c\$).
• Thermal energy storage systems use materials with high specific heat capacities (e.g., water, molten salts) to store large amounts of heat.

Common Misconceptions

1. “All substances heat up at the same rate.” – Incorrect. The rate depends on \$c\$; a material with a low \$c\$ will experience a larger temperature change for the same amount of heat.
2. “Specific heat capacity is the same as heat capacity.” – Heat capacity \$C\$ refers to a particular object (\$C = mc\$), while \$c\$ is an intrinsic property of the material.
3. “Temperature and internal energy are the same thing.” – Temperature measures average kinetic energy per particle; internal energy is the total kinetic energy of all particles.

Practice Questions

1. A 1.5 kg aluminium block is heated from \$25\,°C\$ to \$75\,°C\$. Calculate the heat energy absorbed. (\$c_{\text{Al}} = 900\;J\,kg^{-1}\,K^{-1}\$)
2. Why does a metal spoon become hot faster than a wooden spoon when placed in a cup of hot tea?
3. If \$2000\;J\$ of heat is removed from 0.5 kg of copper, what is the resulting temperature drop? (\$c_{\text{Cu}} = 385\;J\,kg^{-1}\,K^{-1}\$)

Summary

• Increasing the temperature of an object raises its internal energy because particle kinetic energy increases.
• The quantitative link is \$Q = mc\Delta T\$.
• Specific heat capacity is a material property that determines how much heat is needed for a given temperature change.
• Understanding \$c\$ helps explain everyday phenomena and solve exam problems.