# Heat, Work and Energy

## Heat, work and energy tutorial - essentials as specific heat

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### Heat

Heat energy is transferred as a result of a temperature difference. Energy as heat passes from a warm body with higher temperature to a cold body with lower temperature.

The transfer of energy as a result of the temperature difference alone is referred to as **heat flow**. The ** Watt**, which is the SI unit of power, can be defined as

*1*of heat flow.

**J/s**Other units used to quantify heat energy are the

*(the amount of heat to raise*

**British Thermal Unit - Btu***1 lb*of water by

*1*) and the

^{o}F*(the amount of heat to raise*

**Calorie***1 gram*of water by

*1*(

^{o}C*or 1 K*)).

- check temperature for more info about degrees Celsius and degrees Kelvin

Calorie is defined as an amount of heat required to change temperature of *one gram* of liquid water by *one degree Celsius (or one degee Kelvin).*

1 cal = 4.184 J

Units of energy used may be *calorie (cal), Joule (J, SI unit) or Btu.* For comparing units, check the unit converter for more information!

### Specific Enthalpy

This is the term given to the total energy, due to both pressure and temperature, of a fluid (such as water or steam) at any given time and condition. More specifically it is the sum of the internal energy and the work done by an applied pressure.

The basic unit of measurement is the joule (J). Since one joule represents a very small amount of energy it is common to use *kilo Joules (kJ) (1 000 Joules).*

Specific enthalpy is a measure of the total energy of **a unit mass. ** The unit commonly used is *kJ/kg*.

### Heat Capacity

Heat Capacity of a system is the amount of heat required to change the temperature of *the whole* *system* by

*one degree*.

**Specific Heat**

Specific heat is the amount of heat required to change temperature of *one kilogram* of a substance by *one degree*. Specific heat may be measured in *kJ/kg K* or *Btu/lb ^{o}F*. For comparing units, check the unit converter for more information!

Specific heats for different materials can be found in the Material Properties section.

Since enthalpy of a fluid is a function of its temperature and pressure, the temperature dependence of the enthalpy can be estimated by measuring the rise in temperature caused by the flow of heat at constant pressure. The constant-pressure specific heat - *c _{p}* - is a measure of the change in enthalpy at a particular temperature.

Similarly, the internal energy is a function of temperature and specific volume. The constant volume specific heat -

*c*

_{v}- is a measure of the change in internal energy at a particular temperature and constant volume.

Unless the pressure is extremely high the work done by applied pressure on solids and liquids can be neglected, and enthalpy can be represented by the internal energy component alone. Constant-volume and constant-pressure heats can be said to be equal.

For solids and liquids

c_{p}= c_{v}

The specific heat represents the amount of energy required to raise *1 kg by 1 ^{o}C (or 1 K)*, and can be thought of as the ability of a substance to absorb heat. Therefore the SI units of specific heat are

*kJ/kg.K (kJ/kg.*. Water has a very large specific heat of

^{o}C)*4.19 kJ/kg.*compared to many other fluids and materials.

^{o}C**Water is a good heat carrier!**

**Amount of Heat Required to Rise Temperature**

The amount of heat needed to heat a subject from one temperature level to an other can be expressed as:

Q = c_{p}m dT(2)

where

Q= amount of heat (kJ)

c_{p}= specific heat (kJ/kg.K)

m= mass (kg)

dT= temperature difference between hot and cold side (K)

### Example Heating Water

Consider the energy needed to heat *1.0 kg* of water from *0 ^{o}C to 100 ^{o}C* when the specific heat of water is

*4.19 kJ/kg.K (*:

*kJ/kg.*)^{o}C

Q= (4.19 kJ/kg.K) (1.0 kg) ((100^{o}C) - (0^{o}C))

= 419 (kJ)

### Work

The amount of mechanical work done can be determined by an equation derived from Newtonian mechanics

Work = Applied force x Distance moved in the direction of the force

or

W = Fl (3)

where

W = work (Nm (J))

F = applied force (N)

l = length or distance moved (m)

Work can also be described as the product of the applied pressure and the displaced volume:

Work = Applied pressure x Displaced volume

or

W = p A l (3b)

where

p = applied pressure (N/m^{2}(Pa))

A = pressurized area (m^{2})

l = length or distance the pressurized area is moved by the applied force (m)

#### Example - Work done by a Force

The work done by a force *100 N* moving a body *50 m* can be calculated as

*W = (100 N) (50 m)*

* = **5000** (Nm, J)*

The unit of work is joule, J, which is defined as the amount of work done when a force of 1 newton acts for a distance of 1 m in the direction of the force.

1 J = 1 Nm

#### Example - Work due to Gravitational Force

The work done when lifting a mass of *100 kg* an elevation of *10 m* can be calculated as

*W = F _{g} h *

* = m g h *

* = (100 kg) (9.81 m/s ^{2}) (10 m)*

* = **9810** (Nm, J)*

*where *

*F _{g} = force of gravity - or weight (N)*

*g = acceleration of gravity 9.81 (m/s ^{2})*

*h = elevation (m)*

- hydro-power

In imperial units a unit work is done when a weight of *1 lb _{f}*

*(pound-force)*is lifted vertically against gravity through a distance of

*1 foot*. The unit is called

*lb ft*.

An object with mass *10 slugs* is lifted *10 feet*. The work done can be calculated as

*W = F _{g} h *

* = m g h *

* = (10 slugs) (32.17405 ft/s ^{2}) (10 feet)*

* = 3217 lb _{f} ft*

#### Example - Work due to Change in Velocity

The work done when a mass of *100 kg* is accelerated from a velocity of *10 m/s* to a velocity of *20 m/s *can be calculated as

*W = (v _{2}^{2} - v_{1}^{2}) m / 2*

* = ((20 m/s) ^{2} - (10 m/s)^{2}) (100 kg) / 2*

* = **15000** (Nm, J)*

*where *

*v _{2} = final velocity (m/s)*

*v _{1} = initial velocity (m/s)*

### Energy

Energy is the capacity to do work (a translation from Greek-"work within"). The SI unit for work and energy is the joule, defined as *1 Nm*.

- more energy units

Moving objects can do work because they have kinetic energy. ("kinetic" means "motion" in Greek).

The amount of kinetic energy possessed by an object can be calculated as

E_{k}=1/2 m v^{2}(4)

where

m= mass of the object (kg)

v= velocity (m/s)

The energy of a level position (stored energy) is called potential energy. This is energy associated with forces of attraction and repulsion between objects (gravity).

The total energy of a system is composed of the internal, potential and kinetic energy. The temperature of a substance is directly related to its internal energy. The internal energy is associated with the motion, interaction and bonding of the molecules within a substance. The external energy of a substance is associated with its velocity and location, and is the sum of its potential and kinetic energy.

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