Sustainable Energy Fundamentals

Sustainable Energy Fundamentals 1
NUMERICAL PROBLEMS BASED ON THERMODYNAMICS AND ENERGY
FUNDAMENTALS
By Name
Course
Instructor
Institution
Location
Date

Sustainable Energy Fundamentals 2
1- A piston cylinder device contains nitrogen with initial volume, temperature, and pressure of
0.1 m3, 25 °C, and 150 kPa, respectively. The nitrogen is then compressed up to 1 MPa when its
temperature reaches 150 °C. If the compression energy (in the form of work) added to the system
is 20 kJ, calculate the amount of heat transfer during the process and comment on its direction
(find nitrogen specific heats attached if required.
Initial volume, V1 = 0.1m3
Temperature, T1 = 25oC = 198K
Pressure, P1 = 150kPa
After nitrogen compression
Pressure, P2 = 1MPa = 106 Pa
Temperature, T2 = 150oC = 423K
Compression energy = 20kJ
Amount of heat transfer = ?
By assuming an ideal behaviou;
P1 V 1
T 1
= P2 V 2
T 2
150 x 103 x 0.1
290 =106 x V 2
423
V2 = 0.02129 m3
Given that Cp = 29.12 + 0.0027(T - 300)
Cv = R – Cp
= 8.314 – 29.12 – 0.0027(T - 300)
= -20.806 – 0.0027(T - 300) J/molK
μ = P1 V 1
RT1
=¿ 150 x 103
298 x 8.314 = 6.05431 moles
Therefore, ∫ dU=∫
T1
T2
μCvdr
dU = 6.0543 ∫
T 1
T 2
{−20.806−0.0027 T +0.81 }dr
dU= 6.0543{-19.996(423-298)-0.0027(4232-2982)/2}
dU= -15.8693 kJ
Since, δw = -20kJ

Sustainable Energy Fundamentals 3
Hence, δQ = δw + dU
= -15.8693 – 20
= -35.8693 kJ
Direction of Heat Transfer
Therefore, the heat is lost during the process