The First Law

Question 1

Define internal energy (U)

Answer 1

The total energy a system contains as a result of its physical state

Question 2

What does the first law state?

Answer 2

Internal energy of a system is constant unless it is changed by work or by heat transfer

U = q + w

Question 3

What are some characteristics of U?

Answer 3

• U is path independent
• U is a state function
• U is an extensive property
• In microscopic terms, U is equal to the total sum of the energy levels of the atoms or molecules making up the system, weighted by their probabilities of being occupied

Question 4

What is heat?

Answer 4

The transfer of energy due to a difference in temperature between the system and its surroundings.

If Tsystem < Tsurroundings, q is positive

If Tsurroundings > Tsystem, q is negative

Question 5

What is work?

Answer 5

A process which could be used directly to move an object a certain distance against an opposing force

Question 6

Define work of expansion

Answer 6

The work done by the system against the surroundings in moving a piston of area A by distance dz against an opposing force

F(z) = pext(z)A:
dw = -F(z) dz = -pextAdz = -Pext(V)dV

Question 7

What are the characteristics of expansion?

Answer 7

p > pext

Work is negative as the internal energy of the system decreases by carrying work on the surroundings

Question 8

What are the characteristics of compression?

Answer 8

pext > p

Work is positive as the internal energy of the system increases

Question 9

What is the determining factor of work done?

Answer 9

external pressure (pext)

Question 10

What is the work of expansion of a gas against a constant external pressure?

Answer 10

Wext = {pext(V)dv
= -pex deltaV

Work is negative for deltaV postitve

Question 11

How can the system be changed so the reaction is reversible?

Answer 11

pext must be adjusted to be equal to p at each infinitesimal step in the expression

This keeps the system in equilibrium

Question 12

What is the ideal gas equation?

Answer 12

pV = nRT

When T is constant,
Wexp = -nRT{1/v dv = -nRTln(Vf/Vin)

Question 13

How can expansion be carried out irreversibly?

Answer 13

Suddenly lower pext from pa to pb, the expansion occurs against a constant external pressure, pext = pb

The work of expansion is therefore wexp = -pb deltaV

Question 14

In what system does irreversible expansion occur?

Answer 14

Adiabatic or isothermal

Question 15

Compare the wexp in irreversible and reversible reactions

Answer 15

wexp (irr) | < |wexp (rev)|

Question 16

When does a system carry out maximum work?

Answer 16

A system operating between specified initial and final states does the maximum work when the process is carried our reversibly

Question 17

Is work a state functions?

Answer 17

Work is not a state function as different work was done between the same states in Vin and Vf in reversible and irreversible states

Work is a path function

Question 18

Is heat a state function?

Answer 18

Heat is not a state function as different work is done between the same states Tinital and Tfinal in the reversible and irreversible states

Heat is a path function

Question 19

What is a path function?

Answer 19

The values of a path function depend on the path taken between the initial and final states

They are inexact differentials

eg dq and dw

Question 20

How is U different from q and v?

Answer 20

U only depends on the state of the system and is has a definite value which is independent of path taken (it is a state function)

dU is an exact differential

Question 21

How can U be written as a function of T and V

Answer 21

dU = (dU/dx)v dT + (dU/dV) dV

The order of differentiation does not affect the result