## Note on Heat Capacity or Thermal Capacity

• Note
• Things to remember

#### Introduction

Calorimetry is an experimental technique for quantitative measurement of heat exchange. Take a look at the calorimeter shown in a figure. It consists of a cylindrical vessel, generally made of copper and a stirrer of the same material. The calorimeter is well insulated to prohibit the transfer of heat into or out of the calorimeter. So, the vessel is placed inside a wooden box by wrapping it with woolen clothes. A thermometer inserted inside the calorimeter measures the temperature of the content of calorimeter. A calorie is unit of heat in CGS system and joule in SI-units. One calorie is the amount of heat necessary to raise the temperature of one gram of water by one degree Celsius. One calorie is equal to 4.2 joules.

#### Specific Heat Capacity

Consider two different bodies and they are heated of same rate by a burner for an equal time. We will observe that the temperature of two bodies will not be same. So, the amount of heat required to raise the temperature depends on following factors:

Amount of heat Q required to raise the temperature of a substanceis directly proportional to its mass, m

$$\text{i.e.} Q\propto m\dots(i)$$

and depends upon a rise in the temperature,

$$Q\propto\Delta\theta \dots(ii)$$

Combining equations (i) and (ii), we have

$$Q\propto m\Delta\theta$$

$$Q=ms\Delta\theta\dots(iii)$$

Where s is a proportionality constant called specific heat capacity of the substance.

If m= 1kg and $$\Delta\theta = 1^oC$$, then

$$Q =s$$

Thus, the specific heat capacity of a substance is defined as the amount of heat required to change the temperature of unit mass of substance through 1 degree. Its unit is Jkg-1 k-1in SI-system and 1 cal gm-1 C-1 in CGS –system.

 Substance Jmole-1 k-1 cal mole-1 C-1 Aluminum 910 0.215 Copper 390 0.092 Ethanol 2428 0.58 Glass 419 – 837 0.1 – 0.27 Ice(0) 2100 0.5 Iron 470 0.112 Lead 130 0.013 Silver 4200 1 Steam 1926 0.46 Water 4200 1

Heat Capacity or Thermal Capacity

Heat capacity of a substance is defined as the amount of heat required to change its temperature through one degree. It is also called thermal capacity. If Q is the amount of heat required to change the temperature of a body of mass m through, then

$$Q = ms\Delta\theta$$

If the temperature difference =1then

$$Q = ms$$

Its unit is J k-1 in SI-system and cal C-1 in CGS –system.

#### Water Equivalent of a Substance

It is a mass of a body which absorb or emit the same degree rise or fall in temperatures.

Suppose m is the mass of the body which required Q amount of heat to raise the temperature by $$\theta$$. If S is the specific heat capacity of the body then,

$$Q = ms\Delta\theta\dots(i)$$

If w is water equivalent of the body. sw is specific heat capacity of the water. Then, from the definition of water equivalent.

$$Q = ws_w\Delta\theta\dots(ii)$$

Comparing equation (i) and (ii)

$$ws_w\Delta\theta\ =ms\Delta\theta\$$

$$ws_w=ms$$

$$w=\frac{ms}{s_w}$$

In CGS system, specific heat capacity of water, sw = 1 cal g-1 C-1, then

$$w= ms$$

So, water equivalent of a substance is numerically equal to its thermal capacity in CGS-system. But the unit of water equivalent is grams and that of thermal capacity is calories.

Calorimetry is an experimental technique for quantitative measurement of heat exchange.

One calorie is the amount of heat necessary to raise the temperature of one gram of water by one degree Celsius.

Heat capacity of a substance is defined as the amount of heat required to change its temperature through one degree.

Water equivalent of a substance is numerically equal to its thermal capacity in CGS-system.

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200g of water at 100 degreeCelsius is poured into a copper calorimeter containing 150g of water at 10degree Celsius. If the final temperature of the mixture is 45degree Celsius . calculate the thermal capacity of the vessel