What Is the Heat Capacity in an Isothermal Process?

In summary: W: In summary, the question presents a picture and asks for the expression of heat capacity C. The attempt at a solution uses the equations ΔU=n*Cv*(T2-T1) and W=nRT1*ln(V3/V2), but is unable to progress further. The question then asks for the heat capacity at all pressures on the isothermal curve.
  • #1
maurice2705
6
0

Homework Statement


The question is presented as picture.


Homework Equations


What is the expression of this 'heat capacity C'?
The x-process is isothermal then C=nCΔT=0?
Please give me some ideas.

The Attempt at a Solution


set V1=V2, V3=V4, T1=T4, T2=T3, p1+p0=p2, p3-p0=p4
constant volume process:ΔU=n*Cv*(T2-T1)=Cv*V1*p0/R where p0=p2-p1
isothermal process:W=nRT1*ln(V3/V2)=nRT1*ln(p2/p3)
Then I can't go any further.
 

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  • #2
maurice2705 said:

Homework Statement


The question is presented as picture.

Homework Equations


What is the expression of this 'heat capacity C'?
The x-process is isothermal then C=nCΔT=0?
Please give me some ideas.

The Attempt at a Solution


set V1=V2, V3=V4, T1=T4, T2=T3, p1+p0=p2, p3-p0=p4
constant volume process:ΔU=n*Cv*(T2-T1)=Cv*V1*p0/R where p0=p2-p1
isothermal process:W=nRT1*ln(V3/V2)=nRT1*ln(p2/p3)
Then I can't go any further.
Heat capacity is defined as: C = ΔQ/ΔT. Since work is being done but there is no change in internal energy, ΔQ > 0. However, since it is isothermal, ΔT = 0. So what is the heat capacity, ΔQ/ΔT at all pressures (points) on the isothermal curve?

AM
 

Related to What Is the Heat Capacity in an Isothermal Process?

1. What is heat capacity in an ideal engine?

Heat capacity in an ideal engine refers to the amount of heat energy that is required to increase the temperature of the engine by one degree Celsius. It is a measure of the engine's ability to store and transfer heat.

2. How is heat capacity related to engine efficiency?

The heat capacity of an ideal engine is directly related to its efficiency. A higher heat capacity means that the engine is able to store and transfer more heat, resulting in a more efficient conversion of heat energy into mechanical work.

3. What factors affect the heat capacity of an ideal engine?

The heat capacity of an ideal engine depends on several factors, including the type of fuel used, the design and materials of the engine, and the operating conditions such as temperature and pressure.

4. Can the heat capacity of an ideal engine be increased?

The heat capacity of an ideal engine can be increased by optimizing the design and materials used, and by improving the combustion process to produce more heat energy. However, it cannot be increased beyond a certain point due to the laws of thermodynamics.

5. How is heat capacity measured in an ideal engine?

Heat capacity in an ideal engine is typically measured in units of joules per degree Celsius (J/°C) or specific heat capacity in units of joules per kilogram per degree Celsius (J/kg·°C). These measurements can be obtained through experiments or calculated using thermodynamic equations.

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