Concept explainers
A piston–cylinder device contains helium gas initially at 100 kPa, 10°C, and 0.2 m3. The helium is now compressed in a polytropic process (PVn = constant) to 700 kPa and 290°C. Determine the heat loss or gain during this process.
FIGURE P4–123
The heat transfer during the process of piston-cylinder device.
Answer to Problem 123RP
The heat transfer during the process of piston-cylinder device is
Explanation of Solution
Write the expression for mass of helium.
Here, the initial pressure of helium is
Write the expression of ideal gas relation for volume after compression.
Here, the final pressure of helium is
Write the expression of polytropic index by using ideal gas relation.
Here, the polytropic index exponent.
Write the expression of boundary work for the polytropic process.
Here, the final temperature of helium is
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Simplify Equation (V) and write energy balance relation of piston-cylinder device.
Here, the heat to be transfer into the system is
Conclusion:
From the Table A-1 “Molar mass, gas constant, and critical-point properties”, obtain the value of gas constant of helium for piston-cylinder device as
From the Table A-2 “Ideal-gas specific heats of various common gases”, obtain the value of constant-volume specific heat of helium for piston-cylinder device as
Substitute
Substitute
Substitute
Substitute
……
Substitute
Thus, the heat transfer during the process of piston-cylinder device is
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Chapter 4 Solutions
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