Air as an ideal gas is contained in a piston/cylinder system constrained by a non-linear spring. Initially the gas in the cylinder is at 100 kPa, which is balanced by the atmospheric pressure outside of the cylinder (the weight of the piston is negligible). The force on the spring at the start is zero. The spring force is F=kx². k=600. kNt/m². The cross-sectional area of the piston is 1 m², the initial volume is 1 m³, and the initial temperature is 300 K. Heat is added until the volume of the gas has expanded to 1.5 m³. Find: (a) The work done by the gas on the face of the piston (kJ).

Air as an ideal gas is contained in a piston/cylinder system constrained by a non-linear spring. Initially the gas in the cylinder is at 100 kPa, which is balanced by the atmospheric pressure outside of the cylinder (the weight of the piston is negligible). The force on the spring at the start is zero. The spring force is F=kx². k=600. kNt/m². The cross-sectional area of the piston is 1 m², the initial volume is 1 m³, and the initial temperature is 300 K. Heat is added until the volume of the gas has expanded to 1.5 m³. Find: (a) The work done by the gas on the face of the piston (kJ).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.

Question

Air as an ideal gas is contained in a piston/cylinder system
constrained by a non-linear spring. Initially the gas in the cylinder
is at 100 kPa, which is balanced by the atmospheric pressure
outside of the cylinder (the weight of the piston is negligible). The
force on the spring at the start is zero. The spring force is F=kx².
k=600. kNt/m². The cross-sectional area of the piston is 1 m², the
initial volume is 1 m³, and the initial temperature is 300 K. Heat is
added until the volume of the gas has expanded to 1.5 m³. Find:
(a) The work done by the gas on the face of the piston (kJ).
(b) The final temperature (K).
(c) The amount of heat added (kJ).
Hint: This problem is easiest if you calculate the spring work and
the atmospheric work separately.
Air
V₁=1.0 m³
Piston Area = 1.0 m²
T₁=300 K
P₁=100 kPa
Atmospheric P on upper
piston face= 100 kPa

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Step 1: To find a) The work done by the gas, b)Final temperature, c) Amount of heat added. Given, P1=100 kpa

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Step 3: Solution to find the final temperature (T2).

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