|Table of contents|
|Law of Mixture|
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When we say that a body is heated it means that its molecules begin to move with greater kinetic energy.
S.I. unit of heat energy is joule (J). Another common unit of heat energy is calorie (cal).
Specific heat of water: s = 4200 J/kg°C = 1000 cal/kg°C = 1 Kcal/kg°C = 1 cal/gm°C.
Specific heat of steam = half of specific heat of water = specific heat of ice
Example 1. Heat required to increases the temperature of 1 kg water by 20°C
Heat required = ΔQ = msΔθ
= 1 x 20 = 20 Kcal.
∴ S = 1 cal/gm°C = 1 Kcal/kg°C
(a) We know, s = , if the substance undergoes the change of state which occurs at constant temperature (DT = 0), the s = Q/0 = ¥. Thus the specific heat of a substance when it melts or boils at constant temperature is infinite.
(b) If the temperature of the substance changes without the transfer of heat (Q = 0) then s = = 0. Thus when liquid in the thermos flask is shaken, its temperature increases without the transfer of heat and hence and the specific heat of liquid in the thermos flask is zero.
(c) To raise the temperature of saturated water vapour, heat (Q) is withdrawn. Hence, specific heat of saturated water vapour is negative. (This is for your information only and not in the course)
(d) The slight variation of specific heat of water with temperature is shown in the graph at 1 atmosphere pressure. Its variation is less than 1% over the interval form 0 to 100°C.
The heat capacity of a body is defined as the amount of heat required to raise the temperature of that body by 1°C. If `m' is the mass and `s' the specific heat of the body, then
Heat capacity = m s
Units of heat capacity in CGS system is, cal °C-1 ; SI unit is, JK-1
Relation between Specific heat and Water equivalent
It is the amount of water which requires the same amount of heat for the same temperature rise as that of the object
ms AT = mw Sw ΔT
In calorie sw = 1
∴ mw = ms
mw is also represented by W
so W = ms
Law of Mixture
When two substances at different temperatures are mixed together, the exchange of heat continues to take place till their temperatures become equal. This temperature is then called final temperature of the mixture. Here, Heat taken by one substance = Heat given by another substance.
⇒ m1s1(T1 - Tm) = m2s2(Tm - T2)
Example 2. An iron block of mass 2 kg, fall from a height 10 m. After colliding with the ground it loses 25 % energy to surroundings. Then find the temperature rise of the block (Take sp. heat of iron 470 J/kg°C)
Example 3. The temperature of equal masses of three different liquids A, B, and C are 10°C 15°C and 20°C respectively. The temperature when A and B are mixed is 13°C and when B and C are mixed, it is 16°C. What will be the temperature when A and C are mixed?
when A and B are mixed
mS1 x (13 - 10) = m x S2 x (15 - 13)
3S1 = 2S2 ...(1)
when B and C are mixed
S2 x 1 = S3 x 4 ...(2)
when C and A are mixed
S1(θ - 10) = s3 x (20 - θ) ,..(3)
by using equation (1), (2) and (3)
Example 4. If three different liquid of different masses specific heats and temperature are mixed with each other and then what is the temperature mixture at thermal equilibrium.
Sol. Total heat lost or gain by all substance is equal to zero.