heat capacity of an ideal gas and discussion about details of cp and cv

Tell us about the heat capacity and the relation between them..

1. HEAT CAPACITY OF
AN IDEAL GAS

2. •Specific Heat
The specific heat capacity of an object is the amount of energy that
is required to raise the temperature of one gram of substance on
one degree Celsius.
�= ��∆??????
•Molar Heat Capacity
is the amount of heat to raise the temperature of a mole of a
substance.
�= �??????∆??????
REVIEW

3. HEAT CAPACITY OF AN IDEAL GAS
The specific heat or molar heat capacity of a substance depends on the
conditions under which the heat is added.
•The heat capacity of a gas is usually measured in a closed container under
constant-volume conditions. The corresponding heat capacity is the molar
heat capacity at constant volume, denoted by ??????
v
•Heat capacity measurements for solids and liquids are usually carried out
under constant atmospheric pressure, and we call the corresponding heat
capacity the molar heat capacity at constant pressure, ??????
p

4. MEASURING MOLAR HEAT CAPACITY
Constant Volume Constant Pressure
In a constant-volume temperature increase, the system
does no work, and the change in internal energy
∆�equals the heat added �.
??????�=????????????+????????????+0=????????????
In constant-pressure temperature
increase, volume must increase,
so pressure remains constant.

5. pV-Diagram
•It shows the relation of ??????
pand ??????
v
•Raising the temperature of an
ideal gas from T
1to T
2 by a
constant-volume or a constant-
pressure process. For an ideal
gas, U depends only on T, so ∆U
is the same for both processes.
But for the constant-pressure
process, more heat Q must be
added to both increase U and do
work W. Hence ??????
p > C
V.

6. RELATING ??????
??????AND ??????
�FOR AN IDEAL GAS
For constant volume:
??????�=????????????
????????????�
??????�=????????????
????????????�
For constant pressure:
��= �??????
??????�??????
��= ??????��= ���??????
�??????
??????�??????= �??????
��??????+ ���??????
∴??????
??????= ??????
�+ �
The molar heat capacities ??????
??????and ??????
??????of an ideal gas differ by R, the ideal-gas
consant. The dimensionless ratio of heat capacities
??????
??????
??????
??????
, is denoted by ??????.
??????
??????=??????
??????+�
�=????????????∆�

7. THE RATIO OF HEAT CAPACITY
MONATOMIC GASES
??????
??????=
3
2
�
??????
??????=??????
??????+�=
5
2
�+�=
5
2
�
∴??????=
??????
??????
??????
??????
=
5
2
??????
3
2
??????
=
5
3
= 1.67
DIATOMIC GASES
??????
??????=
5
2
�
??????
??????=??????
??????+�=
5
2
�+�=
7
2
�
∴??????=
??????
??????
??????
??????
=
7
2
??????
5
2
??????
=
7
5
= 1.40

8. EXAMPLE1
Find the change in the internal energy of this much air when it is cooled
from 35.0°C to 26.0°C at a constant pressure of 1.00 atm.
Treat the air as an ideal gas with g = 1.400.

9. EXAMPLE 2
Three moles of an ideal monatomic gas expands at a constant pressure
of 2.50 atm, the volume of the gas changes from 3.20×10
−2
??????
3
to
4.50×10
−2
??????
3
.
(a)Calculate the initial and find temperatures of the gas.
(b)Calculate the amount of work the gas does in expanding.
(c)Calculate the amount of heat added to the gas.
(d)Calculate the change in internal energy of the gas.