Specific Heat Capacity

2.2.2 Specific Heat Capacity

Specific heat capacity (c) is the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 °C. It is a material property.

Measuring the Specific Heat Capacity of a Solid

One method to measure the specific heat capacity of a solid involves calorimetry. A calorimeter is an insulated container designed to minimize heat exchange with the surroundings.

Experimental Setup:

1. A known mass of the solid is heated to a known initial temperature ($T_i$).
2. The solid is then rapidly and efficiently transferred to a calorimeter containing a known mass of water ($m_w$) at a known initial temperature ($T_i$, which is assumed to be the same as the solid's initial temperature).
3. The calorimeter is insulated to minimize heat loss.
4. The temperature of the water-solid mixture is monitored until it reaches a maximum temperature ($T_f$).

Data Required:

• Mass of the solid ($m_s$)
• Initial temperature of the solid ($T_i$)
• Mass of the water ($m_w$)
• Initial temperature of the water ($T_i$)
• Final temperature of the mixture ($T_f$)
• Specific heat capacity of water ($c_w = 4.18 J/kg°C$)

Calculations:

Assuming the calorimeter is perfectly insulated, the heat lost by the solid is equal to the heat gained by the water. Therefore:

$$Q_{lost} = m_s \times c_s \times \Delta T$$ $$Q_{gained} = m_w \times c_w \times \Delta T$$

Where $\Delta T = T_f - T_i$. Equating these gives:

$$m_s \times c_s \times (T_f - T_i) = m_w \times c_w \times (T_f - T_i)$$

Solving for the specific heat capacity of the solid ($c_s$):

$$c_s = \frac{m_w \times c_w \times (T_f - T_i)}{m_s \times (T_f - T_i)} = \frac{m_w \times c_w}{m_s}$$

Measuring the Specific Heat Capacity of a Liquid

Similar to a solid, the specific heat capacity of a liquid can be determined using calorimetry.

Experimental Setup:

1. A known mass of the liquid is heated to a known initial temperature ($T_i$).
2. The liquid is then transferred to a calorimeter containing a known mass of water ($m_w$) at a known initial temperature ($T_i$, which is assumed to be the same as the liquid's initial temperature).
3. The calorimeter is insulated to minimize heat loss.
4. The temperature of the water-liquid mixture is monitored until it reaches a maximum temperature ($T_f$).

Data Required:

• Mass of the liquid ($m_l$)
• Initial temperature of the liquid ($T_i$)
• Mass of the water ($m_w$)
• Initial temperature of the water ($T_i$)
• Final temperature of the mixture ($T_f$)
• Specific heat capacity of water ($c_w = 4.18 J/kg°C$)

Calculations:

Using the same principle as for a solid, the heat lost by the liquid is equal to the heat gained by the water:

$$Q_{lost} = m_l \times c_l \times \Delta T$$ $$Q_{gained} = m_w \times c_w \times \Delta T$$

Where $\Delta T = T_f - T_i$. Equating these gives:

$$m_l \times c_l \times (T_f - T_i) = m_w \times c_w \times (T_f - T_i)$$

Solving for the specific heat capacity of the liquid ($c_l$):

$$c_l = \frac{m_w \times c_w \times (T_f - T_i)}{m_l \times (T_f - T_i)} = \frac{m_w \times c_w}{m_l}$$

Property	Solid	Liquid
Heat lost by the substance	$Q_{lost} = m_s \times c_s \times \Delta T$	$Q_{lost} = m_l \times c_l \times \Delta T$
Heat gained by the water	$Q_{gained} = m_w \times c_w \times \Delta T$	$Q_{gained} = m_w \times c_w \times \Delta T$
Specific heat capacity of the solid	$c_s = \frac{m_w \times c_w}{m_s}$	N/A
Specific heat capacity of the liquid	N/A	$c_l = \frac{m_w \times c_w}{m_l}$