# Calorimetry and Change of State

## Introduction

1. • Deals with measurement of heat.$\\$• Based on conservation of energy.$\\$• The bodies originally at higher temperature losses$\\$heat while the other body gains heat.$\\$i.e. Heat lost by one body = Heat gained by another body. This is known as the principle of calorimetry.$\\$• Quantity of heat is measured in Joule/calorie.$\\$

• 1 Cal=4.2 Joule$\\$

2. $\textbf {Formula for Calorimetry:} \\$Q=mc∆T$\\$Where,$\\$Q = heat evolved (heat absorbed − heat released) in joules (J)$\\$m = mass in kilograms (kg)$\\$c = specific heat capacity in J/k°C (or J/kg⋅K)$\\$∆T = temperature change in °C (or K)

## Specific Heat Capacity

Specific heat capacity is defined as the amount of heat required to raise the$\\$temperature of 1 kilogram of a substance by 1 kelvin or 1 degree Celsius.$\\$CGS unit is calorie per gram per degree Celsius & SI unit it is Joule$\\$per kg per degree kelvin.$\\$S$_{gas}$>S$_{liquid}$>S$_{solid}$$\\$•Specific heat of water =4200 J/kgK or 1 Cal/gmK$\\$• Specific heat of ice= 2100J/KgK or 0.5 cal/gmK$\\$•Heavier the element smaller the specific heat(Sp. heat * At wt=6.4)

## Thermal capacity

The thermal capacity of a body is the heat necessary to raise the$\\$temperature of the body by one degree.$\\$T.C=m.c, where m=mass, c=specific heat capacity. It’s unit is J/K or Cal/C.

Water Equivalent:
A substance's water equivalent is equivalent to the amount$\\$of water that is required to consume the same quantity of heat as that substance$\\$does for a temperature rise of one degree.$\\$Water equivalent of body = mass of body x specific heat capacity.$\\$Dimensionally it is equal to thermal capacity

## Molar Heat Capacities

1. \textbf{Amount of heat per mole necessary to increase the unit temperature. In the case of gas, heat lost or gained by body is given by\$At Constant Volume$\\$Q = n Cv ∆T$\\$ At Constant Pressure$\\$Q = n Cp ∆T$\\$• \gamma = \dfrac[𝐶_𝑝}{𝐶_𝑣}\$

• 𝐶𝑝 -𝐶𝑣=R (Mayer’s relation)$\\$

• $\gamma$ is 1.67 for monoatomic gases, 1.4 for diatomic gases, and 1.33 for$\\$polyatomic gases.

## Latent heat

1. •Heat required for changing state of substance without changing in temperature.$\\$• Isothermal Process.$\\$•No change in state.$\\$•Q=mL.$\\$

2. $\textbf {Latent heat of fusion:} \\$•From solid to liquid.$\\$• For ice it is 80cal/g.$\\$

3. $\textbf {Latent heat of vaporization:} \\$•From liquid to gas.$\\$•For boiling water it is 540cal/g.$\\$

4. $\textbf {Effect of pressure on melting of solid:} \\$Melting point increases with increase in pressure for substances like Sulfur,$\\$Glass, Ghee, wax. (Expands on melting).$\\$Melting point decreases with increase in pressure for substance like Ice, Rubber.$\\$(Contracts on melting).$\\$Effect of Pressure on boiling point of liquid.$\\$With increase in pressure boiling point of all increases.

## Hygrometry

1. A branch of physics that deals with the measurement of humidity especially of$\\$the atmosphere.$\\$The maximum limit of water vapor that a given quantity of air can hold at a particular temperature$\\$is termed as saturated vapor.$\\$In such a case, relative humidity will be 100 percent.$\\$For all other cases, where maximum limit of vapour is not reached, the vapor$\\$thus formed is termed as unsaturated vapor.$\\$

2. $\textbf {Triple Point:} \\$In chemistry and physics, the triple point is the temperature and pressure at$\\$which solid, liquid, and vapor phases of a particular substance coexist in$\\$equilibrium. It is a specific case of thermodynamic phase equilibrium.$\\$The triple point for water is at 0.01 degree Celsius at 4.56 mm Hg and constant.

3. $\textbf {Dew Point:} \\$Temperature at which vapor actually present in atm is sufficient to saturate it.$\\$

4. $\textbf {Absolute Humidity:} \\$Amount of water vapor actually present in the unit volume is called Absolute humidity.$\\$

5. $\textbf {Relative Humidity:} \\$The amount of water vapor present in air expressed as a percentage of the$\\$amount needed for saturation at the same temperature.$\\$R.H= $\frac{m}{M}$ *100% Also R.H= $\frac{p}{P}$*100%; Where p=SVP at dew point and P=svp at room temperature$\\$(SVP is saturated vapor pressure)

1. SVP(Saturated Vapour Pressure) < UVP(Unsaturated vapor Pressure) [Always]$\\$

2. Specific heat of substances under isothermal condition is infinite. [During change in state]$\\$

3. Specific heat under adiabatic condition is zero[Q=0]$\\$

4. Melting point decreases on addition of soluble impurities and increases on$\\$addition of soluble impurities.$\\$

5. Regelation is the process of melting of ice due to increase in pressure and$\\ resolidification after removal of pressure.$\\$

6. Bottle opened on the moon starts boiling.$\\$

7. A large iceberg melts at the base but not at the top because due to high$\\$pressure, ice at the base lowers its mpt.$\\$

8. Generally Cp>Cv but when water is heated from 0-4 Cv>Cp and at 4 degree$\\$Celsius Cp=Cp.$\\$

9. Evaporation decreases temperature.$\\$

10. Water is used to cool the radiators of the engine.$\\$

11. In high Himalaya it takes longer to cook than in the valley(Because of Pressure).$\\$

12. Boiling Water extinguishes fire very quickly.$\\$

13. R.H is low in dry air and high in moist air.$\\$

14. If the door of the fridge is opened the temperature of the room increases.$\\$

15. A man feels hottest when relative humidity is near 100%.$\\$

16. Heat required to convert 1 gm of ice at 0 degree Celsius to steam of 100 degree celsius is 716cal.$\\$

17. Specific heat of the same substances is expressed in two units $C_1$ cal/gC and $C_2$cal/gF then $C_1$=$C_2$

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