Lecture 5Lecture 5First Law of ThermodynamicsFirst Law of Thermodynamics

First Law of ThermodynamicsFirst Law of Thermodynamics

You can’t get something for nothing.

Nothing is for free.

We will discuss these statements later…

Thermodynamic SystemThermodynamic System

Consider a closed system (e.g., a parcel of air).

It has internal energy (“u”) = energy due to molecular kinetic and potential energies.

Suppose some energy (dq) is added to the system.

Example: via radiation from the sun

What happens?

Thermodynamic SystemThermodynamic System

Some of the energy goes into work done (dw) by the system against its surroundings.

Example: expansion

What’s left is a change in internal energy.

du = dq – dw

Conservation of Energy principle

“nothing is for free”

Thermodynamic SystemThermodynamic System

System

EnvironmentHeat

System can exchange energy with environment via heat flow.

Thermodynamic SystemThermodynamic System

In addition, system can do work on environment or vice versa.

Example: expansion

First Law, General FormFirst Law, General Form

dU = dQ – dWdU = dQ – dW

dU = change in internal energy of systemdU = change in internal energy of system

dQ = heat exchanged with environmentdQ = heat exchanged with environment dQ > 0 dQ > 0 heat flowing into system heat flowing into system

dW = work done by or on systemdW = work done by or on system dW > 0 dW > 0 system is doing work system is doing work

Ideal GasIdeal Gas

Consider a system consisting of an ideal Consider a system consisting of an ideal gas in a cylinder.gas in a cylinder.

Cylinder has a piston, which allows Cylinder has a piston, which allows volume to be changed.volume to be changed.

CylinderCylinderweights

more weight, more pressure

Gas

Walls of cylinder:

1) perfect heat conductors

2) perfect insulators

CasesCasesCase 1: Walls of cylinder are perfect Case 1: Walls of cylinder are perfect conductorsconductors heat can freely flow between system and heat can freely flow between system and

environmentenvironment in equilibrium, temperature of system must in equilibrium, temperature of system must

equal temperature of environmentequal temperature of environment

Case 2: Walls of cylinder are perfect Case 2: Walls of cylinder are perfect insulatorsinsulators no heat flow between system and no heat flow between system and

environmentenvironment temperatures of system and environment temperatures of system and environment

need not be equalneed not be equal

Work (Qualitative)Work (Qualitative)

System does work on environment System does work on environment (dW > 0) if gas expands(dW > 0) if gas expands (Piston is pushed upward.)(Piston is pushed upward.)

Work is done on system (dW < 0) if Work is done on system (dW < 0) if gas contractsgas contracts (Piston is pushed downward.)(Piston is pushed downward.)

Work (Quantitative)Work (Quantitative)

Suppose piston is pushed upward a distance dx.Suppose piston is pushed upward a distance dx.

Work (Quantitative)Work (Quantitative)

Suppose piston is pushed upward a distance dx.Suppose piston is pushed upward a distance dx.

dx

Area of piston = A

Pressure force = pA

dW = pAdx

= pdV

First Law, Ideal GasFirst Law, Ideal Gas

dVpdQdU Usually, we are interested in energy per unit mass

Divide both sides by m

Define u = U/m; q = Q/m; = V/m

First Law, Ideal Gas (per unit mass)First Law, Ideal Gas (per unit mass)

dpdqdu

Internal EnergyInternal Energy

For an ideal gas, For an ideal gas, uu is a function of T only is a function of T only u is an increasing function of Tu is an increasing function of T

Change in internal energy depends only Change in internal energy depends only on change in temperature.on change in temperature. Doesn’t depend on the way in which that Doesn’t depend on the way in which that

temperature change is accomplished.temperature change is accomplished. du = kdu = kdT, where k is a constantdT, where k is a constant (Value of k will be determined shortly.)(Value of k will be determined shortly.)

Heat Capacity, CHeat Capacity, C

dT

dQC

For a gas, C depends on the particular process.

Cv = heat capacity at constant volume (dV = 0)

Cp = heat capacity at constant pressure (dp = 0)

SI units: JK-1

Amount of heat required to change a “body’s” temperature by a given amount

Specific HeatSpecific Heat

Specific heat is heat capacity Specific heat is heat capacity per unit massper unit mass

ccvv (lower case) = specific heat at constant (lower case) = specific heat at constant

volumevolume

ccpp = specific heat at constant pressure = specific heat at constant pressure

Specific heat is the heat energy needed to Specific heat is the heat energy needed to raise the temperature of a unit mass of a raise the temperature of a unit mass of a substance by one degree. substance by one degree.

Specific HeatSpecific Heat

vv dT

dqc

dT

dq

Suppose we add some thermal energy (dq) to a unit mass of a substance like air, water, soil.

We expect T(substance) to increase

How much?

We can define Specific Heat as

Heat added

Temp change

pp dT

dqc

Constant volume Constant pressure

Specific Heat of Dry AirSpecific Heat of Dry Air

ccvv = 717 J = 717 Jkgkg-1-1KK-1-1

ccpp = 1004 J = 1004 Jkgkg-1-1KK-1-1

Note: cNote: cpp – c – cvv = 287 J = 287 Jkgkg-1-1KK-1-1

Look familiar?Look familiar? ccpp – c – cvv = R = Rdd

(Not a coincidence!)(Not a coincidence!)

Constant Volume ProcessesConstant Volume Processes

pddqdu 0

Tdcdqdu v

Internal Energy ChangeInternal Energy Change

The following is The following is alwaysalways true: true:

Tdcdu v (3.40) W&H

First Law for Ideal Gas, Re-writtenFirst Law for Ideal Gas, Re-written

dpdqdTcv (1)

Constant-Pressure ProcessesConstant-Pressure Processes

Go back to ideal-gas law:Go back to ideal-gas law:

RTp Take differential of both sides:

dTRpd )(

But,…But,…

dpdppd )(

dpdTRpd (2)

Substitute (2) into (1)Substitute (2) into (1)

dpdqdTcv

dpdTRpd

dpdTRdqdTcv

SimplifySimplify

dpdqdTRcv

0dpConstant-pressure process

dTRcdq v

(3)

But, …But, …

dTcdq p

For a constant-pressure process,

CompareCompare

dTRcdq v and

dTcdq p

Result: Rcc vp

Rewrite (3)Rewrite (3)

dpdqdTc p We will use this in the next lecture.

(4)