# Heat

Heat is a form of energy. It can transfer from one object to another if they are at different temperatures. Heat transfers spontaneously from an object at a higher temperature to an object at a lower temperature but not in the opposite direction.

#### Unit of heat

Since heat is an energy, its SI unit is joules (J). Other common, non-SI unit of heat is calories (cal). If you want to raise the temperature of an object, you need to add heat to the object. 1 calorie is defined as the amount of heat required to raise the temperature of 1 gram of water by 1 °C, standardized as from 14.5 °C to 15.5 °C. The conversion factor from calorie to J is 1 cal. = 4.186 J. The unit calorie used in food labels is called food calorie. 1 food cal. = 1000 cal.

#### Specific heat

To raise the temperature of a substance, a heat must be added to it. But how much heat is required ? It depends upon three things: (1) amount (mass) of the substance, i.e., more substance means more heat requires to raise its temperature, (2) temperature difference $(\Delta T)$ between the object and the heat source and (3) the material of the substance, i.e., some materials require more heat than other to raise the temperature to the same level. If we take into account all these, we arrive at the following equation for the amount of heat $Q$ required to raise the temperature of an object by an amount, $\Delta T$,

$Q=mc\Delta T$

where $c$ is called the specific heat of the material of the object. Specific heat is a material property, for water, specific heat is 4186 J/kg/°C and for iron, it is 450 J/kg/°C. Since water has a higher value of specific heat capacity than iron, water requires more heat than iron to change its temperature to the same amount.

### Types of systems

There are three types of systems regarding the mass and the energy of the system: open system, closed system and isolated closed system. In an open system, mass and energy can enter or leave the system. In a closed system, there is no transfer of mass in and out of the system, but the energy can transfer. If there is no transfer of mass and energy in or out of the system, then we call that an isolated closed system. Since, in an isolated closed system, there is no transfer of mass and energy in or out of the system, any heat lost by one object is gained by other objects in the system. i.e., the net heat transfer is zero in an isolated closed system:

$Q_{net}=0$

or

$Q_{lost}+Q_{gain}=0$

or

$Q_{lost}=-Q_{gain}$

For example, if we add ice into water, water loses some heat and the ice gain that lost heat.

#### Calorimetry and calorimeter

Calorimetry is a technique to quantitatively measure the heat exchange in a system. The instrument used for calorimetry is called a calorimeter. Calorimeter is used to measure the heat exchange and the specific heat capacity of substances. It contains a cup and a stirrer placed in an insulated enclosure to avoid heat exchange with the surroundings. Since there is no heat transfer outside the system, we consider it is an isolated closed system.

### Latent heat

Latent heat is the heat required to change the phase of a substance. Consider a piece of ice at some temperature, say -25°C. You want to have some liquid water at say 15°C from the ice. That is you need to raise the temperature of the ice from -25°C to 15°C. For that you are adding some heat. If you use a thermometer to measure the temperature of the ice while you heat, you will see the temperature rise until the temperature reaches 0 °C. But once the temperature reaches this temperature, you will not see any change in temperature until all the ice melted. That means, whatever the heat that you added to the substance at the on set of melting to the complete melting is just used to change the phase of ice, i.e., from ice at 0 °C to water to at 0 °C. Since this heat is not showed as temperature rise, we call this latent heat. Latent means not visible. Latent heat does not increase the temperature of an object, but it only changes the phase.

Latent heat $(L)$ of a substance is defined as the amount of heat required to change the phase of $1 kg$ of the substance. If there is $m$ kg of substance then the required heat for phase change is

$Q=mL$

Since there are three different phases (solid, liquid and gas), there are three different latent heats associated with each phase change: latent heat of fusion, latent heat of vaporization and latent heat of sublimation.

Latent heat of fusion, $L_F$ is the heat required to change the phase of 1 kg of a substance from solid to liquid. So, the heat required to change the phase of m kg of substance from solid to liquid is

$Q=mL_F$

If the phase of the substance changes in the reverse order, i.e, from liquid to solid, same amount of heat is released. Since the heat leaves the substance, the final temperature is lower than the initial temperature and you need to add a minus sign, i.e., $Q=-mL_F$.

Latent heat of vaporization, $L_V$ is the heat required to change the phase of 1 kg of a substance from liquid to vapor, and the latent heat of sublimation, $L_S$ is the heat required to change the phase of 1 kg of a substance from solid to vapor.

### Heat transfer

There are three ways by which heat can transfer from one object to another. They are conduction, convection and radiation.

#### Conduction

When two objects are in contact, heat is transferred between the objects if they are at different temperatures. Such a heat transfer between objects in contact is called conduction. In conduction, heat is transferred by means of molecular collisions. Molecules at the hotter side moves/vibrates at higher rates and collide with neighboring molecules and transfer the heat.

The amount of heat transfer by conduction per unit time is called the heat conduction rate. In the above figure, heat is conducted from an object at a higher temperature, $T_H$ to an object at a lower temperature, $T_L$. The heat is conducted through another object (the blue object) in between them. The heat conduction rate is given by Fourier's equation,

$\dfrac{Q}{t}=kA\:\dfrac{T_H-T_L}{l}$

where $A$ is the area of cross section through which the heat conduction takes place (i.e., the area of cross section of the blue object), $l$ is the distance between the hot and the cold object (length of the blue object), i.e., the thickness of the object in between the two main objects and $k$ is the thermal conductivity of the material through which the heat conduction takes place (the thermal conductivity of the blue object).

Thermal conductivity is a material property. For glass, thermal conductivity is 0.84 J/s.m.°C. From the above equation, if you consider, during the winter time, the heat conduction between the inside and outside of a room of a house, the thicker window (i.e., the larger $l$) reduces the heat conduction rate and also the smaller window (i.e., smaller area $A$), reduces the heat conduction through the window.

#### Convection

Convection is a heat transfer process by bulk movement of molecules from one place to another. For example, at home the heat is carried by the movement of hot air molecules from one place to another from a heater.

Radiation is the transfer of heat energy from one place to another without any medium in between. For example, the sun transfer heat energy to the earth by radiation. There is no material medium is necessary between the sun and the earth to have sun light here on earth. All objects emit radiation if the temperature is greater than 0 K.

Amount of heat radiated from an object per unit time is called the radiation rate. An object at an absolute temperature $T$ radiates (emits) heat energy at the rate:

$\dfrac{Q}{t}=\epsilon \sigma AT^4$

where $A$ is the surface area of the object, $\epsilon$ is the emissivity of the object, for a perfect emitter $\epsilon =1$. Note that the $T$ is the absolute temperature, i.e., in kelvin.

The above equation is called Stefan-Boltzmann equation.

An object that emits radiation also absorbs radiation. Rate of absorption depends on the temperature of the environment. Rate of heat absorbed by an object in an environment of temperature, $T_0$ is

$\dfrac{Q}{t}=\epsilon \sigma AT_0^4$

If you subtract the absorption rate from the radiation (emission) rate, you will get the net radiation rate. Net heat radiation rate of an object at temperature $T$ is therefore,

$\dfrac{Q}{t}=\epsilon \sigma A(T^4-T_0^4)$