# How to Calculate Work and Heat Transfer in a Polytropic Process of Nitrogen?

• ZLing
In summary, the question is asking us to calculate the work and heat transfer for a polytropic process with given initial and final pressure and temperature. The work can be calculated by integrating PdV and the heat transfer can be found using the first law of thermodynamics, knowing the change in internal energy and work. To find the work, V1 and V2 need to be determined first.
ZLing

## Homework Statement

Nitrogen at 100°C and 600 kPa expands in such a way it can be approximated by a polytropic process with n=1.2. Calculate the work and the heat transfer if the final pressure is 100 kPa.

## The Attempt at a Solution

I used the equation T2/T1=(P2/P1)^[(n-1)/n] to find T2. Then i used W=nCv(T1-T2) to calculate work done. Is this correct? But i don't know how to calculate the heat transfer.

ZLing said:

## Homework Statement

Nitrogen at 100°C and 600 kPa expands in such a way it can be approximated by a polytropic process with n=1.2. Calculate the work and the heat transfer if the final pressure is 100 kPa.

## The Attempt at a Solution

I used the equation T2/T1=(P2/P1)^[(n-1)/n] to find T2. Then i used W=nCv(T1-T2) to calculate work done. Is this correct?
No. This is not the work. This is the change in internal energy. To get the work, you need to integrate PdV.
But i don't know how to calculate the heat transfer.
If you know the change in internal energy and the work, then you can use the first law to get the heat.

Chet

Chestermiller said:
No. This is not the work. This is the change in internal energy. To get the work, you need to integrate PdV.

If you know the change in internal energy and the work, then you can use the first law to get the heat.

Chet
Hi, does that mean I have to find V1 and V2 first?

ZLing said:
Hi, does that mean I have to find V1 and V2 first?
That's one way to start.

Chet

## 1. What is a Polytropic Process of Nitrogen?

A polytropic process of nitrogen is a thermodynamic process in which the gas undergoes a change in its pressure and volume while following a specific equation known as the polytropic law. This equation relates the pressure and volume of a gas undergoing a reversible process.

## 2. What is the polytropic law for nitrogen?

The polytropic law for nitrogen is represented by the equation P1V1^n = P2V2^n, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index. This index can vary from 0 to ∞ and represents the type of process (isothermal, adiabatic, isobaric, etc).

## 3. How does a polytropic process of nitrogen differ from other thermodynamic processes?

A polytropic process of nitrogen differs from other thermodynamic processes in that it follows a specific equation, the polytropic law, and can have a variable polytropic index. This allows for a more accurate representation of the process, as it takes into account the specific conditions of the system.

## 4. What are the applications of the polytropic process of nitrogen?

The polytropic process of nitrogen has many applications in various industries, such as in gas turbines, refrigeration systems, and air compressors. It is also used in the production and storage of liquid nitrogen, as well as in the study of gas dynamics and thermodynamics.

## 5. How is the polytropic process of nitrogen related to the ideal gas law?

The polytropic process of nitrogen is related to the ideal gas law, as it is a specific case of this law. The ideal gas law states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature. The polytropic law is a variation of this equation, taking into account the polytropic index.

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