LIBRARY

PRODUCTS

FORUMS

CART

Join CodeCogs

Or login with:

Engineering › Thermodynamics ›

Second Law of Thermodynamics

States the Second law and goes on to proove the Carnot Principle

View version details

Contents

Introduction
Carnot's Principle.
Page Comments

Introduction

This concerns the quality of heat as measure by temperature. The Law states:

Heat can not be transferred from a body at a lower temperature to a body at a higher temperature without the application of enery from an external source.

Available Energy

This is the proportion of heat supplied to a machine which can be converted into mechanical work. This portion is found to depend upon the temperature of the source of heat and the temperature at which heat is rejected

Carnot's Principle.

This states that no machine can be more efficient than a machine working under a thermodynamically reversible cycle, provided that they are both working under the same limits of temperature. All reversible engines have the same efficiency when working between the same temperature limits.

Proof

Consider two engines E and R. E works under an irreversible cycle whilst R's is reversible. Assume that E is more efficient than R

E takes

units of heat at temperature

and converts

into work.

is rejected to a heat sink at temperature

Efficiency, $\displaystyle \eta _E=\frac{W}{Q}$

R takes $(Q+\delta Q)$ units of heat at temperature

and converts

into work $(Q+\delta Q-W)$ is rejected to the heat sink at a temperature of

Efficiency, $\displaystyle \eta _R=\frac{W}{Q + \delta Q}$ , and this must be less than $\eta _E$

Reversing the process in the reversible engine R

R takes $(Q-W+\delta Q)$ units of work to drive it backwards and rejects $(Q+\delta Q)$ at a temperature

Now use the work output of engine E to provide the power to drive R backwards.

If this to be an isolated system within which no external work is being achieved, and $\delta Q$ units of heat are being transferred from the cold sink to the hot sink. Then this will contradict the Second Law, therefore the original assumption can not be true.

Page Comments

You must login to leave a messge