Specific Heat (Heat)

THERMAL CAPACITY AND WATER EQUIVALENT

1. The quantity of heat required to raise the temperature of a given substance by 1°C is called its thermal capacity or heat capacity.
It is the product of mass and specific heat.
Units: \( cal^0 C^{ - 1} ,JK^{ - 1} \)
Dimensions: \( ML^2 T^{ - 2} K^{ - 1} \)
2. The mass of water in grams which would require the same amount of heat to raise its temperature through 1°C as the body when heated through the same temperature is called water equivalent.
3.In CGS system, thermal capacity and water equivalent are numerically equal.
4. Thermal capacity = ms=\(\frac {Q} {\theta}\)  or  \( \frac{{dQ}} {{d\theta }} \)

SPECIFIC HEAT
The quantity of heat required by one gram of a substance to raise its temperature by 1°C is called its specific heat (s).
Units:  S.I unit of specific heat = J kg^–1 K^–1
CGS unit of specific heat is cal g^–1 °C^–1     
Dimensions: \( M^0 L^2 T^{ - 2} K^{ - 1} \) .

Some points related to specific heat:
1. Of all solids and liquids water has the highest specific heat.  Its value is 1 cal gm °C or 4180 J Kg K (J=4.18 J/Cal). 
2. Specific heat of ice is 0.5 cal gm^{-1 0}c^-1    or 2090 J  Kg^-1 K^-1
Specific heat of steam is 0.45 cal gm^{-1 0}c^-1   or 188J  Kg^-1 K^-1
3.Of all gases hydrogen has the highest specific heat (3.5 cal gm^{-1 0}c^-1   )
Specific heat of a substance during its change of state is infinity.
Specific heat of a substance depends on temperature and nature of material.
(In general for heavier materials it is less)
Specific heat of saturated water vapour is negative. ie in order to raise the tempera- ture, it loses a certain quantity of heat.
As the temperature of water increases from 0°C to 100°C, its specific heat decreases upto 35°C (minimum) and after that increases.
4. According to Dulong and Petit, product of specific heat of an element in the solid state and its atomic weight is about 6.4cal gm^{-1 0}c^-1  
5. As specific heat of water is more, it is used in radiators and hot water bags.
6. In liquids specific heat is minimum for mercury.
7. Heat lost or gained by a substance is Q = ms\(\theta\)  m is mass, s is specific heat and \(\theta\) is change in temperature.
Specific heat s=\( \frac{Q} {{m\theta }} \) (or) s =\( \frac{1} {m}\frac{{dQ}} {{d\theta }} \)
8. If two substances of masses m₁,m₂ specific heats s₁,s₂ at initial temperatures \(\theta_1,\theta_2\) are mixed then final temperature of the mixture is
           \( \frac{{m_1 s_1 \theta _1 + m_2 s_2 \theta _2 }} {{m_1 s_1 + m_2 s_2 }} \) (no heat losses)
9. If two liquids of specific heats s₁,s₂ having masses m₁,m₂ are mixed at the same temperature, effective specific heat of the mixture is s=\( \frac{{m_1 s_1 + m_2 s_2 }} {{m_1 + m_2 }} \)
If \( m_1 = m_2 \) then s=\( \frac{{s_1 + s_2 }} {2} \)
If  \( V_1 ,V_2 \) are volumes and \( d_1 ,d_2 \) are their densities, s =\( \frac{{d_1 V_1 s_1 + d_2 V_2 s_2 }} {{d_1 V_1 + d_2 V_2 }} \)
here if  \( V_1 = V_2 \) then s=\( \frac{{d_1 s_1 + d_2 s_2 }} {{d_1 + d_2 }} \)
10. If same quantity of heat is given to two different substances and \( \theta _1 ,\theta _2 \)  are the changes in their temperatures, \( m_1 s_1 \theta _1 = m_2 s_2 \theta _2 \)
11. Specific heat is also known as specific heat capacity. 
12. At the boiling point specific heat of water is infinity.
13. Heat lost or gained by a system depends not only on the initial and final states but also on the path taken by that process.
14. When heat is supplied to a body, if greater the specific heat of a substance, lesser will be the change in temperature.