First and Second Laws of Thermodynamics

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RAT 11b

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Class Objectives

Understand and apply:work, energy, reversibility, heat capacityFirst and Second Laws of Thermodynamics

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Reversibility

Reversibility is the ability to run a process backwards and forwards infinitely without losses.

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Reversible Irreversible (no service fee) (5% service fee)Day Dollars Pounds Dollars PoundsMonday 100.00 40.00 100.00 38.00Tuesday 100.00 40.00 90.25 34.30Wednesday 100.00 40.00 81.45 30.95Thursday 100.00 40.00 73.51 27.93Friday 100.00 40.00 66.34 25.20

Each morning, dollars are converted to pounds.Each evening, pounds are converted to dollars.

Money analogy

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Using Excel, reproduce the previous table, except use a service charge of 10%.

Pair Exercise 1

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Reversibility and Energy

If irreversibilities were eliminated, these systems would run forever.Perpetual motion machines

Electric Current

Generator Motor

Voltage

Pump Turbine

Fluid Flow

Pressure

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Example: Popping a Balloon

A “reversible process” can go in either direction, but these processes are rare.

Generally, the irreversibility shows up as waste heat

Not reversible unless energy is expended

XNot reversible

without expendingenergy

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Sources of Irreversibilities

Friction Voltage drops Pressure drops Temperature drops Concentration drops

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Basic Laws of Thermodynamics

First Law of Thermodynamicsenergy can neither be created nor

destroyed Second Law of

Thermodynamicsnaturally occurring processes are

directional

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First Law of Thermodynamics

One form of work may be converted into another,

or, work may be converted to heat, or, heat may be converted to work, but, final energy = initial energy

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2nd Law of Thermodynamics

We intuitively know that heat flows from higher to lower temperatures and NOT the other direction.i.e., heat flows “downhill” just like waterYou cannot raise the temperature in

this room by adding ice cubes. Thus processes that employ heat are

inherently irreversible.

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Heat/Work Conversions

Heat transfer is inherently irreversible. This places limits on the amount of work that can be produced from heat.

Heat can be converted to work using heat enginesJet engines (planes), steam engines

(trains), internal combustion engines (automobiles)

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Heat into Work

A heat engine takes in an amount of heat, Qhot, and produces work, W, and waste heat Qcold.

Nicolas Carnot (kar nō) derived the limits of converting heat into work.

High-temperatureSource, Thot

Low-temperatureSink, Tcold

HeatEngine

W

QhotQcold

(e.g., flame) (e.g., cooling pond)

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Carnot Equation: Efficiency

Given the heat engine on the previous slide, the maximum work that can be produced is governed by:

where the temperatures are absolute temperatures.

Thus, as Thot Tcold, Wmax 0. This ratio is also called the efficiency, .

hot

cold

hot

max

T

T

Q

W1

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Pairs Exercise 2

Use Excel to create a graph showing the amount of work per unit heat for a heat engine in which the source temperature increases from 300 K to 3000 K and the waste heat is rejected to an ambient temperature of 300 K.

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Work into Heat

Although there are limits on the amount of heat converted to work, work may be converted to heat with 100% efficiency.

This is shown by Joule’s experiment…

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Joule’s Experiment

Joule’s Mechanical Equivalent of Heat

F

m

x

This proved 1 kcal = 4,184 J

1 kg H2O

T = 1oC

E = Fx = 4,184 J

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Where did the energy go?

By the First Law of Thermodynamics, the energy we put into the water (either work or heat) cannot be destroyed.

The heat or work added increased the internal energy of the water.

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Internal Energy

Translation

Rotation

Vibration

MolecularInteractions

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Heat Capacity

An increase in internal energy increases the temperature of the medium.

Different media require different amounts of energy to produce a given temperature change.

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Heat Capacity Defined

Heat capacity: the ratio of heat, Q, needed to change the temperature of a mass, m, by an amount T:

Sometimes called specific heat

Tm

QC

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Heat Capacity for Constant Volume Processes (Cv)

Heat is added to a substance of mass m in a fixed volume enclosure, which causes a change in internal energy, U. Thus,

Q = U2 - U1 = U = m Cv TThe v subscript implies constant volume

Heat, Qaddedm m

Tinsulation

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Heat Capacity for Constant Pressure Processes (Cp)

Heat is added to a substance of mass m held at a fixed pressure, which causes a change in internal energy, U, AND some PV work.

Heat, Qadded

T

m m

x

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Cp Defined

Thus,Q = U + PV = H = m Cp T

The p subscript implies constant pressure

Note: H, enthalpy. is defined as U + PV, so dH = d(U+PV) = dU + VdP + PdV

At constant pressure, dP = 0, so dH= dU + PdV

For large changes at constant pressure

H = U + PV

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Experimental Heat Capacity

Experimentally, it is easier to add heat at constant pressure than constant volume, thus you will typically see tables reporting Cp for various materials (Table 21.2 in Foundations of Engineering).

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Pair Exercise 3

1. Calculate the change in enthalpy per lbm of nitrogen gas as its temperature decreases from 500 oF to 200 oF.

2. Two kg of water (Cv=4.2 kJ/kg K) are heated using 200 Btu of energy. What is the change in temperature in K? In oF?