Specific Heat

1
Specific Heat

• Thermodynamics
• Professor Lee Carkner
• Lecture 8

2
PAL 7 Work

• Net work of 3 process cycle of 0.15 kg of air in
  a piston
• Isothermal expansion at 350 C from 2 MPa to 500
  kPa
• isothermal work PVln(V2/V1)
• Get V from PV mRT
• V1 (0.15)(0.287)(623) / (2000) 0.01341 m3
• V2 (0.15)(0.287)(623) / (500) 0.05364 m3
• W (2000)(0.01341)ln(0.95364/0.01341)

3
PAL 7 Work

• Polytropic compression with n 1.2
• Need the final volume
• P2V2n P3V3n
• V3 ((500)(0.05364)1.2 / 2000)(1/1.2)
• W (P3V3-P2V2)/1-n (2000)(0.01690)-(500)(0.0536
  4) /(1-1.2)
• Isobaric compression
• W PDV (2000)(0.01341-0.01690)
• Net work 37.18-34.86-6.97

4
Internal Energy of Ideal Gases

• We have defined the enthalpy as
• but Pv RT, so
• So if u is just a function of T then h is too

5
Temperature Dependence of cP
6
Ideal Gas Specific Heats

• We define the specific heat as
• So then we can solve for the change in internal
  energy
• du cv dT
• If the change in temperature is small
• Where cv is the average over the temperature range

7
Linear Approximation of c
8
Using Specific Heats

• We can write a similar equation for h
• Dh cp DT
• Either specific heat
• Is tabulated
• Are generally referenced to 0 at 0K

9
cv is Universal
10
Specific Heat Relations

• We can relate cp and cv
• dh du RdT
• cp cv R
• For molar specific heats
• The specific heat ratio
• k cp/cv

11
Solids and Liquids

• Volume is constant
• This means
• c still is temperature dependent

12
Incompressible Solid
13
Incompressible Enthalpy

• We can write out the enthalpy change expression
  for constant v
• Dh du vdP Pdv du vdP
• For solids the pressure does not change much and
  so

14
Enthalpy of Liquids

• Heaters (constant pressure)
• DP 0
• Pumps (constant temperature)
• DT 0

15
Next Time

• Test 1
• For Monday
• Read 5.1-5.3
• Homework Ch 5, P 12, 15, 20