Isothermal Compression of an Ideal Gas in a Frictionless PCD

In summary, the conversation discusses the compression of 1 mol of nitrogen to a tenth of its original volume isothermally at 300 K in a frictionless piston-cylinder. Two different approaches for calculating the compression work are shown, one using an energy balance approach and the other using a specific volume-pressure relationship. The corresponding heat flow is zero, but if the piston-cylinder experiences significant friction, the heat and work flows will increase to overcome the friction. The two different approaches cannot be used for a cylinder with friction, and a more complex approach is needed.
  • #1
Nah346
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A frictionless piston-cylinder compresses 1 mol of nitrogen to a tenth of its original volume isothermally at 300 K. Assume nitrogen is an ideal gas with Cp*=(7/2)R.

(a) Show two different approaches to calculate the compression work required.
(b) What is the corresponding heat flow?
(c) If the piston-cylinder now experiences significant friction, how will the heat and work flows be different in order to accomplish the same thermodynamic change?
(d) Can the two different approaches in (a) be used to calculate the compression work for a piston cylinder with significant friction? Explain.
 
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  • #2
(a) Two different approaches to calculate the compression work required:1. Using an energy balance approach: The work done is equal to the change in internal energy, since no heat is exchanged with the surroundings. The change in internal energy of the nitrogen is U2-U1=Cv(T2-T1)= (5/2)R(T2-T1). Since T2=T1=300K, the work done is zero.2. Using a specific volume-pressure relationship: The work done is equal to the integral of PdV. The pressure-volume relationship for an ideal gas is PV=nRT, so the work done is W=∫PdV=∫nRT/VdV=nRTln(V2/V1)=nRTln(1/10). Substituting n=1 mol, R=8.314 J/mol K, and V1=10V2, the work done is W=-83.14 J.(b) The corresponding heat flow is zero, since the process is isothermal.(c) If the piston-cylinder experiences significant friction, the heat and work flows will be different in order to accomplish the same thermodynamic change. The work done will increase due to the additional friction, while the heat flow will increase as well to provide the energy necessary to overcome the friction.(d) The two different approaches in (a) cannot be used to calculate the compression work for a piston cylinder with significant friction, since they assume no friction. A more complex approach would be needed to take into account the effect of friction on the heat and work flows.
 

FAQ: Isothermal Compression of an Ideal Gas in a Frictionless PCD

1. What is isothermal compression?

Isothermal compression is a process in which an ideal gas is compressed at a constant temperature, resulting in a decrease in volume and an increase in pressure.

2. What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are directly proportional to each other. It also assumes that there are no intermolecular forces between gas particles and that the gas particles occupy negligible volume.

3. What is a frictionless PCD?

A frictionless PCD (piston-cylinder device) is a device used in thermodynamics experiments, where a gas is compressed or expanded by a piston in a cylinder. In this case, the PCD is assumed to have no friction, meaning that there is no resistance to the movement of the piston.

4. What are the applications of isothermal compression?

Isothermal compression has various applications in industries such as refrigeration, air conditioning, and gas storage. It is also used in thermodynamics experiments to study the behavior of gases under constant temperature conditions.

5. How does isothermal compression differ from adiabatic compression?

The main difference between isothermal and adiabatic compression is that isothermal compression occurs at a constant temperature, while adiabatic compression occurs without the exchange of heat with the surroundings. This means that in isothermal compression, the temperature remains constant, while in adiabatic compression, the temperature increases due to the compression process.

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