# Heat, Work and Energy

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

### Heat (Energy)

The SI-unit of heat - or energy - is * joule (J)*.

With temperature difference

- heat will transfer from a warm body with higher temperature to a colder body with lower temperature

Other units used to quantify heat are the * British Thermal Unit - Btu* (the amount of heat to raise

*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*)).

A **calorie** is defined as the amount of heat required to change the temperature of *one gram* of liquid water by *one degree Celsius (or one degree Kelvin).*

1 cal = 4.184 J

### Heat Flow (Power)

Heat-transfer as result of temperature difference alone is referred to as **heat flow. **The SI units for heat flow is * J/s* or

*- the same as power.*

**watt (W)****is defined as**

*One watt*

*1 J/s**.*

### Specific Enthalpy

Specific Enthalpy is a measure of the total energy in **a unit mass. ** The SI-unit commonly used is ** J/kg** or

**.**

*kJ/kg*The term relates 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 enthalpy is the sum of internal energy and work done by applied pressure.

### 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 (= specific heat capacity) is the amount of heat required to change temperature of *one* *mass unit* of a substance by *one degree*.

Specific heat may be measured in ** J/g K, J/kg K, kJ/kg K, cal/gK** or

**and more.**

*Btu/lb*^{o}F*Never use tabulated values of heat capacity without checking the unites of the actual values!*

Specific heat for common products and materials can be found in the Material Properties section.

#### Specific Heat - Constant Pressure

The enthalpy - or internal energy - of a substance is a function of its temperature and pressure.

The change in internal energy with respect to change in temperature at fixed pressure is the *Specific Heat at constant pressure - c _{p}.*

#### Specific Heat - Constant Volume

The change in internal energy with respect to change in temperature at fixed volume is the Specific Heat at constant volume - *c _{v}*.

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}(1)_{}

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

*J/kgK (kJ/kg*. Water has a 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/kgK)

m= mass (kg)

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

**Example Heating Water**

Consider the energy required 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*^{o}C

Q= (4.19 kJ/kg) (1.0 kg) ((100^{o}C^{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)*

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.