Heat and Work

In more general terms, all energy in a thermodynamic system can be classified as either heat or work.

Heat is thermal energy that is transferred across the boundary of systems with differing temperatures, always in the direction of the lower temperature. Heat transfer occurs when two adjacent bodies of mass are not in equilibrium due to a difference in temperature. Heat is commonly expressed in calories or British thermal units.

• British thermal unit (Btu) is the amount of energy required to raise the temperature of 1 lbm of water by 1.0°F, standardized at 60°F (i.e., from 59.5°F to 60.5°F).

• Calorie (c) is the amount of heat necessary to raise the temperature of 1 gram of water from 14.5°C to 15.5°C.

Other commonly used heat units, which are defined below under the definition of work, are the Joule (J) and the Watt-hour (Wh). In SI units, kilo (k) and mega (M) are used to indicate 1,000 and 1,000,000 units, respectively (e.g., kcal, kJ, kWh, MJ, and MWh). Correspondingly, in English units, M and MM are used to indicate 1,000 and 1,000,000 units, respectively (e.g., MBtu and MMBtu).

Work (w), or mechanical energy, is done when a force acts through a distance. Work is the product of force and the displacement along the line of force. Doing work requires the expenditure of energy. Ft-lbf, Joule (J), horsepower-hour (hp-h), and kWh are the common measures of work. A Joule is the amount of energy equal to the work done by a force of 1 Newton (N) when the point at which the force is applied is displaced 1 meter in the direction of the force. This is also known as 1 Newton-meter of energy.

The following terms are useful in more fully understanding the concept of work.

Force (F) is the action that will cause acceleration of a mass. Change in velocity of an object is caused by force. If no force acts on an object, it moves at constant velocity. Newton's first law of motion states that a body at rest will stay at rest and a body in uniform motion will continue its uniform motion unless acted upon by a force. Force, expressed in pound-force (lbf) or in Newton (N), is the product of the mass of an object (m) and its acceleration (a) caused by that force. Mass, expressed in lbm slugs, or kilograms (kg), is a measure of the quantity of matter of which an object is composed. Acceleration, expressed in feet per second per second (ft/s2) or in meters per second per second (m/s2), is a measure of the time rate of change of velocity. Thus:

Torque is the force applied at a distance from an axis of rotation and is expressed in lbf-ft or Newton-meter (N-m). It is the product of, for example, the force applied to a lever, or crank arm, and the perpendicular distance from the line of action of the force to the axis of rotation. In rotating machines, the forces required to accelerate (or decelerate) the speed of rotation add up to a torque that is proportional to the angular acceleration times the moment of inertia of the machine.

Power (P) is the rate of doing work and is given by the formula:

dt where power (P) is equal to the rate of energy expenditure (dE) over a given time interval (dt). Thus, power refers to the rate of mechanical energy expenditure over a given time interval or the rate of doing work.

In rotating machines, power is equal to torque times the speed of rotation. Therefore, if speed is held constant, torque and power are proportional. Commonly used units for expressing power are Btu per hour (Btu/h), Joule per second (J/s), ft-lbf per minute (ft-lbf/m), meter-kg per minute (m-kg/m), horsepower (hp), and Watt (W).

• Horsepower (hp) is an English system unit based on the power needed to raise a weight of 550 lbm through a height of 1 foot in 1 second (550 ft-lbm of energy per second) and was originally derived from the estimated power of one horse pulling a load. One hp is approximately equal to 2,545 Btu/h and 745.7 Watt. Brake power is a measure of the power generated by a prime mover. It can be measured at the crankshaft or the flywheel. The term brake refers to a mechanical arrangement used to measure the output torque, which, when multiplied by rotational speed, yields the power.

• Watt (W) is the unit of power equal to 1 J/s and approximately 3.413 Btu/h. 1 kilowatt (kW) is approximately equal to 1.34 hp.

• Metric horsepower (PS) is the power that raises a mass of 75 kg through a height of 1 meter in 1 second. One PS is approximately equal to 0.9863 hp and 735.5 Watt.

Given that power is the rate of doing work, applying a unit of time to a unit of power yields a measure of work. Hence, hp-h or Wh are the common work units. Given that power already has a unit of time, work expressions can be reduced to basic energy units such as Btu, calorie, or Joule. In many thermodynamic applications, Btu is considered to be a more convenient English system unit than ft-lbf. In terms of potential work energy, it is defined by the relationship 1 Btu = 778.16 ft-lbf. One hp is approximately equal to 2,545 Btu. The Joule, which may be considered the mechanical equivalent to heat, is equal to 4.1855 calories.

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