# Polytropic Process: Solving for p1 with p2, T1, T2 & n

• Tux9876
In summary, the conversation is about a question regarding a polytropic process, where the pressure and volume of a gas are related by an equation. The question asks to find an expression for P1 in terms of P2, T1, T2, and n. The answer involves basic algebra and the calculation of T using information about the substance.
Tux9876
Hi,

I have a question relating to a polytropic process. The question consists of two parts.

It says that the pressure (p) and the volume (v) of a gas undergoing a polytropic process are related by the equation:

p1V1^n = p2V2^n (where P1, P2 etc are individual variables as i don't know how to put sub text into the question)
the question then says...where n is the polytropic index.

IF

p1V1/T1 = p2V2/T2

determine an expression for p!, in terms of p2,T1,T2 and n

I have had a look on the net for help in answering the question but not luck so far.

I am assuming that you want to find P1 and not P factorial. This should be basic algebra (I hope). It looks like it could be a bit of a trick question because usually you just deal with P and V in a polytropic compression. To calculate T you need to know about the substance.

If $$P_1 V_1^n = P_2 V_2^n$$ Then

$$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$$

$$\frac{P_1 V_1^n}{T_1}=\frac{P_2 V_2^n}{T_2}$$

$$P_1 = \frac{P_2 T_1}{T_2} \left[ \frac{V_2}{V_1} \right] ^n$$

Last edited:

Hi there,

I can provide some insight into your question about the polytropic process. The polytropic process is a thermodynamic process in which the pressure and volume of a system are related by the equation p1V1^n = p2V2^n, where n is the polytropic index.

In order to solve for p1 in terms of p2, T1, T2, and n, we can use the ideal gas law, which states that pV = nRT, where p is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Using this equation, we can rewrite the given equation as:

p1V1/T1 = p2V2/T2

p1 = (p2V2/T2)*(T1/V1)

Next, we can substitute in the ideal gas law for both p1 and p2:

p1 = (n1RT1/V1)*(T1/V1)

p2 = (n2RT2/V2)*(T2/V2)

Where n1 and n2 are the number of moles of gas at the initial and final states, respectively.

Now, we can combine these equations to solve for p1:

p1 = (n2RT2/V2)*(T2/V2)*(T1/V1)*(V1/n1RT1)

p1 = p2*(T2/T1)*(V1/V2)^(n-1)

Therefore, the expression for p1 in terms of p2, T1, T2, and n is:

p1 = p2*(T2/T1)*(V1/V2)^(n-1)

## 1. What is a polytropic process?

A polytropic process is a thermodynamic process in which the relationship between pressure and volume is described by the equation pV^n = constant, where p is the pressure, V is the volume, and n is a constant known as the polytropic index.

## 2. What is the significance of solving for p1 in a polytropic process?

Solving for p1, the initial pressure, allows us to determine the state of the system at the beginning of the process. This information can then be used to calculate other parameters, such as work and heat transfer, for the system.

## 3. How do I solve for p1 using p2, T1, T2, and n?

The equation for a polytropic process can be rearranged to solve for p1: p1 = p2 * (T1/T2)^(n/(n-1)). Simply substitute the given values for p2, T1, T2, and n into the equation to find p1.

## 4. Can the polytropic index, n, vary during a process?

Yes, the polytropic index can vary during a process depending on the conditions and properties of the system. In some cases, n may be constant, while in others it may change as the process evolves.

## 5. How is a polytropic process different from an isothermal process?

In an isothermal process, the temperature remains constant while the pressure and volume may change. In a polytropic process, the temperature may also change, and the relationship between pressure and volume is described by a power law instead of being constant.

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