Physics · Chapter 11
Study notes aligned to the official NEB syllabus.
The quantity of heat $Q$ required to change the temperature of a body is found to be:
Combining these:
$$Q = m s,\Delta T$$
where the constant of proportionality $s$ is the specific heat capacity of the substance:
$$s = \frac{Q}{m,\Delta T}$$
If $m = 1\ \text{kg}$ and $\Delta T = 1\ \text{K}$, then $s = Q$. Hence the specific heat capacity of a substance is the amount of heat required to raise the temperature of unit mass of the substance by one degree (1 K or 1 °C).
The heat capacity of a body is the amount of heat required to raise the temperature of the whole body by one degree. Setting $\Delta T = 1$ in $Q = m s,\Delta T$:
$$\text{Heat capacity} = m s$$
So heat capacity is the product of the mass and the specific heat capacity of the body. Its SI unit is $\text{J K}^{-1}$.
When two bodies at different temperatures are placed in contact, the hotter body loses heat and the colder body gains heat until both reach a common temperature. If no heat is exchanged with the surroundings, then:
$$\text{Heat lost by hot body} = \text{Heat gained by cold body}$$
This is the principle of calorimetry (a statement of conservation of energy for heat exchange).
A solid heated in a steam jacket (Regnault's apparatus) to a known temperature is transferred to water in a calorimeter and the mixture is stirred to a final temperature. Let:
By the principle of calorimetry:
$$ \begin{aligned} m_s s_s (T_1 - T) &= (m_w s_w + m_c s_c)(T - T_2) \ \boxed{s_s = \frac{(m_w s_w + m_c s_c)(T - T_2)}{m_s (T_1 - T)}} \end{aligned} $$
Knowing $s_w$ and $s_c$, the specific heat of the solid is found.
The quantity of heat required to change the temperature of a body is found to be:
Combining these:
where the constant of proportionality is the specific heat capacity of the substance:
If and , then . Hence the specific heat capacity of a substance is the amount of heat required to raise the temperature of unit mass of the substance by one degree (1 K or 1 °C).
The heat capacity of a body is the amount of heat required to raise the temperature of the whole body by one degree. Setting in :
So heat capacity is the product of the mass and the specific heat capacity of the body. Its SI unit is .
When two bodies at different temperatures are placed in contact, the hotter body loses heat and the colder body gains heat until both reach a common temperature. If no heat is exchanged with the surroundings, then:
This is the principle of calorimetry (a statement of conservation of energy for heat exchange).
A solid heated in a steam jacket (Regnault's apparatus) to a known temperature is transferred to water in a calorimeter and the mixture is stirred to a final temperature. Let:
By the principle of calorimetry:
Knowing and , the specific heat of the solid is found.