Boundary work

1. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
First law of thermodynamics
Polytropic process
Isentropic process
Isothermal process
Isobaric process
Isochoric process

2. Energy (E)
Heat (Q)
𝐻2 − 𝐻1
𝐻𝑔 − 𝐻𝑓
= 𝐻𝑓𝑔
m*C*ΔT
m*Cv*ΔT
m*Cp*ΔT
ሶ
𝑚 * H.V
Work (W)
T * 𝜔
1
2
𝑘(x2
2
− 𝑥1
2
)
ሶ
𝑊 = 𝑉 ∗ 𝐼
Internal
Energy (U)
Kinetic Energy
(KE)
1
2
𝑚𝑉2
Potential
Energy (PE)
M*g*z
Moving Flow
Work
P*V
▪Polytropic process
▪Isentropic process
▪Isothermal process
▪Isobaric process
▪Isochoric process
Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com

3. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
▪Polytropic process
▪Isentropic process
▪Isothermal process
▪Isobaric process
▪Isochoric process
Expansion and compression work is often called moving boundary work
𝒅𝑾=𝑷×𝒅𝑽

4. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
P=f(V)

5. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
𝑷𝑉𝑛=𝑪,where n and C are constants. Polytropic process 𝑷1V1
𝑛
= 𝑷2V2
𝑛

6. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
(n=𝜸)
𝑷𝑉𝑛=𝑪
Polytropic process
Isentropic process
Adiabatic (Q=0) and Reversible (S=C)
𝜸 is the specific heat ratio = 𝑪𝒑/𝑪𝒗
Isothermal process
(n=𝟏)
Isobaric process
(n=0)
Isochoric process
(n=∞)
P
v
𝑃𝑉 = 𝑚ℝ𝑇

7. Ahmed Medhat - Thermodynamics 1 - ahmedhatfa@hotmail.com
Air expanded according to 𝑷𝑉1.33=𝑪 from 5 bar, 227℃ to 1 bar, and then heated at constant
pressure to original temperature.
Determine total work done and amount of heat transferred
Solution
𝑷𝑉𝑛=𝑪
P
v
1
2 3
𝑤𝑡𝑜𝑡𝑎𝑙 = 𝑤1:2 + 𝑤2:3
𝑃𝑉 = 𝑚ℝ𝑇
0.287
1 kg
𝑉2 = ? ?
𝑉1 = 0.284 𝑚3
𝑉3 = 1.421 𝑚3
𝑇2 = 335 𝐾 = 62 ℃ 𝑉2 = 0.952 𝑚3
=
−505 ∗0.952+101 ∗0.284
1−1.33
+ 101 1.421 − 0.952 = +1417.3 𝑘𝐽 𝑎
+47.4 KJ
+1369.9 KJ
𝑞𝑝𝑜𝑙=
ϒ−𝑛
ϒ−1
* 𝑤𝑝𝑜𝑙 +239.5 KJ
𝑞𝑖𝑠𝑜𝑏𝑎𝑟𝑖𝑐= 𝑐𝑝 ∗ (𝑑𝑇 ) +165.825 KJ