Thermodynamics: the first law

Question 1

Define the internal energy of a system

Answer 1

Internal energy (U) is made up of kinetic energy and rotational/vibrational/potential energies

Question 2

Define a change in the internal energy of a system

Answer 2

ΔU = U_final - U_initial = q + w

q = heat transfer

w = work done

Question 3

Describe how the signs are affected by the direction of energy transfer

Answer 3

Energy entering the system is positive and energy exiting the system is negative

Question 4

Define work (w)

Answer 4

Energy transfer through orderly motion of the atoms eg a moving piston

Question 5

Define heat (q)

Answer 5

Energy transfer through random thermal motion of the atoms, eg a hot metal block

Question 6

State the name for an isolated system and its value of q

Answer 6

An isolated system is said to be adiabatic, q = 0

Question 7

Describe the boundary between a system and its surroundings if heat transfer takes place

Answer 7

The boundary must be diathermic (ie must allow heat transfer)

Question 8

Describe volume work, w

Answer 8

If a gas expands quickly, it will cool down.

If a gas is compressed quickly, it will heat up.

work (J) = force (N) x distance (m) = -pressure (Nm^-2) x volume change (m³)

Ie w = -p_exΔV where p_ex is the external pressure

Question 9

Describe the special case of free expansion

Answer 9

p_ex = 0

w = 0

This the case for expansion into a vacumm

Question 10

Describe a reversible change in thermodynamics

Answer 10

A reversible change is one that can be reversed by an infinitesimal modification of a variable.

The system is in equilibrium with the surroundings before and after the change

For the piston example, this means p = p_ex

Question 11

Describe the reversible expansion of an ideal gas at constant temperature

Answer 11

By integrating p over ΔV and substituting p for the ideal gas equation we get w.

note: if we plot p against V, w is the area under the curve

Question 12

Define enthalpy

Answer 12

Enthalpy is the heat obtained from a chemical reaction

ΔH = ΔU + pΔV

Question 13

Define and give examples of state functions

Answer 13

A state function is a property that only depends on the current state and not the path taken to get there.

p,T,V,U,H,S and G are all state functions. w and q are not. w and q are path dependent variables

Question 14

Describe general functions of U and H

Answer 14

U = f(V,T)

H = f(p,T)

Question 15

Define heat capacity, C

Answer 15

C is the amount of heat needed to raise the temperature of a substance by one degree

Question 16

Define a calorie

Answer 16

A calorie, or cal, is defined as the amount of heat needed to raise the temperature of 1g of water by 1 degree

Question 17

Define C at constant volume

Answer 17

Question 18

Define C at constant pressure

Answer 18

Question 19

Go through the steps of finding the difference between C_v and C_p

Answer 19

Question 20

Give C_p in terms of C_v

Answer 20

C_p = C_v + nR

Question 21

State the equipartition principle

Answer 21

For each ‘degree of freedom’ we get ½RT per mole

Question 22

State how many degrees of freedom an ideal gas has and relate this to U

Answer 22

An ideal gas has 3 degrees of freedom

U = 3/2 RT

Question 23

Define π_T in thermochemistry and specifically for an ideal gas

Answer 23

π_T is internal pressure. For an ideal gas it is equal to 0 as there are no interactions