First Law of Thermodynamics

• Introduction• First Law of Thermodynamics• Calculation of Work• PVT diagrams• Thermodynamic processes• Simple Examples• The “everything” problem• More examples

Perspective• Governs theoretical energy & statistical limits, not engineering

details (we’re not “Click and Clack” www.cartalk.com)

• If fuel releases 100 kJ energy– cannot get more than 100 kJ mechanical work (First Law)– cannot get even 100 kJ mechanical work (Second Law)

• (some heat must flow from hot to cold)

• If heat pump does 100 kW mechanical work– Can obtain at least 100 KW heat (First Law)– Can obtain more than 100 kW heat (Second Law)

• (can combine work with heat “pumped” from cold to hot)

• 2 Fundamental Rules– Energy must be conserved - First Law – Must be statistically probable - Second Law

First Law of Thermodynamics• First Law Thermodynamics

– U internal energy, ΔU change in internal energy.– Q is non-mechanical heat, in or out.– W is mechanical work, in or out.

• Don’t let screwy sign convention spook you!– Q is positive in, negative out– W is negative in, positive out.

• Negative sign in first law “flips” that• Negative work in increases U• Positive work out decreases U• Convention used so expansion does positive work

• Example 15-1– Heat added to system 2500 J, work done on system -1800 J

+Q -W

+W-Q

U U

Work by expanding gas• Work done on piston for constant pressure

(Physics 103)

• In general

PVT diagrams – Viewing P,V,T

• Plot pressure vs. volume curves at constant temperature.

• Different PV curves for different temperatures. T is a “parameter”.

• Constant temperature curves called “isotherms”

• Isotherms also lines of constant internal energy. .

• If you return to same isotherm, you return to same temperature and internal energy.

PVT diagrams – Viewing Worka) For constant pressure

– Positive moving to right (volume increasing)

– Negative moving to left (volume decreasing)

– Also area under curve

b) For non-constant pressure

– Area under curve

– Positive moving to right (volume increasing)

– Negative moving to left (volume decreasing)

– Zero (volume remaining constant)

PVT diagrams – Filling in the Heat• Constant pressure expansion

– Work is positive

– Temperature, Internal Energy change positive.

– Heat must be doubly positive

• Constant temperature expansion

– Work is positive

– Temperature, Internal Energy change zero

– Heat in equals work out

• Q is fudge factor that makes up difference.

Thermodynamic Processes I• Isovolumetric pressure increase

– Pressure increase at constant volume

– Higher isotherm, Higher temperature and internal energy

– Heat in

• Isobaric expansion– Volume increase as constant pressure.

– Higher isotherm, Higher temperature and internal energy

– Heat doubly in

Thermodynamic Processes II• Isothermal expansion

– Volume increase as constant temperature.

– out– Same isotherm, constant temperature

and internal energy

– Heat in equals work out

• Adiabatic expansion– Volume increase with no heat exchange. – out– Drop to lower temperature and internal

energy to match work out.

4 thermodynamic paths • A= isovolumetric

– Volume constant.– Pressure drop. – Lower temperature and U.– No work.

• D= isobaric– Volume increase.– No Pressure change.– Higher temperature and U.– Work out.

• C= isothermal– Volume increase.– Pressure decrease.– No temperature U and change.– Work out.

• B = adiabatic– Volume increase.– Pressure decrease.– Temperature and U decrease.– Work out.

Example 15-5 (1)

• Work done in path BD

(in)

• Work done in path DA

(no volume change)

• Internal Energy change BDA

(no temperature change)

• Heat Flow BDA (out)

Example 15-5 (2)• Work done in path AB

(work out)

• Internal Energy change BA

(no temperature change)

• Heat Flow BA (heat in)

• More work out during AB than in during BDA

• Heat in during AB, Heat out during BDA

Example 15-6

• Internal Energy change

• First Law for Q= 0

The “everything” problem• One mole of an ideal gas undergoes the series of processes shown in the figure. (a) Calculate

the temperature at points A, B, C and D. (b) For each process A B, B C, C D, and D A, calculate the work done by the process. (c) Calculate the heat exchanged with the gas during each of the four processes. (d) What is the net work done during the entire process? (e) What is the net heat added during the entire process? (f) What is the thermodynamic efficiency?

“Everything” problem – calculate temperatures & Internal Energies

“Everything” problem – calculate works

• For paths ab and cd pressure is constant

• For paths bc and da volume is constant

“Everything” problem – fill in 1st law tableΔU Work Q

a -> b +6000 J +4000 J

b -> c -4500 J 0 J

c -> d -3000 J -2000 J

d -> a +1500 J 0 J

“Everything” problem – fill in Q’sΔU Work Q

a -> b +6000 J +4000 J 10000 J

b -> c -4500 J 0 J -4500 J

c -> d -3000 J -2000 J -5000 J

d -> a +1500 J 0 J 1500 J

entire cycle 0 J 2000 J 2000 J

• Net work during entire cycle 2000J

• Net heat absorbed/expelled during cycle 2000 J

• Change in internal energy during cycle 0 J

• Net Heat in equals net work out.

• Change in internal energy zero

“Everything” problem – getting efficiencyΔU Work Q

a -> b +6000 J +4000 J 10000 J

b -> c -4500 J 0 J -4500 J

c -> d -3000 J -2000 J -5000 J

d -> a +1500 J 0 J 1500 J

entire cycle 0 J 2000 J 2000 J

• Net work during entire cycle 2000J

• Net heat absorbed/expelled during cycle 2000 J

• Change in internal energy during cycle 0 J

• Efficiency (common sense)

“Everything” problem – Shortcut for ΔUsΔU Work Q

a -> b +6000 J +4000 J

b -> c -4500 J 0 J

c -> d -3000 J -2000 J

d -> a +1500 J 0 J

Animations• Add heat, increase temperature/pressure at constant volume.

• Add heat, increase temperature/volume at constant pressure.

• Add and remove heat, expand and compress gas. (Otto cycle)

idealgas.jnlp

gam2s2_6.swf

otto.swf

Problem 10

a) Do A and C agree on temperature? No. Point C should be 10.7 L

b) What is work done abc?

c) What is change of internal energy abc?

d) What is heat flow abc?

Problem 10 (cont)

e) What is work done ac?

f) What is change of internal energy ac?

d) What is heat flow ac?

Problem 11

a) Find temperature at 1 and 2

b) Find 1-step work from 1 to 2

c) Find 1-step internal energy change 1 to 2

d) Find 2-step internal energy change 1 to 2

Problem 12

• Find ΔU along curvy path

• Work along abc -48 J, find heat along path abc

• Pc = ½ Pb, find heat along path cda

• Since

Questions?

•