# Calculate Work (w) for Isothermal Gas Expansion/Compression

• IoFawkes
In summary, to calculate the work done when 6.5L of an ideal gas at an initial pressure of 34.3atm is expanded or compressed isothermally to a final volume of 34.3L reversibly, we can use the equation w=-nRT In(V2/V1) and substitute PV for nRT. Since nRT is constant for an isothermal process, PV for any state along the process will have the same value. Therefore, we can use PV as our values for P and V in the equation. This means that the work done is equal to the change in PV between the initial and final states.
IoFawkes

## Homework Statement

Calculate Work(w) when 6.5L of an ideal gas at an initial pressure of 34.3atm is expanded or compressed isothermally to a final volume of 34.3L reversibly. Answer in J

PV=nRT
P1V1=P2V2
w=-nRT In(V2/V1)

## The Attempt at a Solution

Using w=-nRT In(V2/V1)
I'm not given mols or T, I know T=constant, since it's isothermal
Can I use PV=nRT and substitute (PV) in for (nRT) in the equation: w=-nRT In(V2/V1) ?
If so, what should I use for values of P and V? Final/Initial/delta?

Io

PS: This may be in the wrong place, the boundary seems unclear in Chem/Phys or Phys/Chem studies.

Welcome to PF!
IoFawkes said:
Can I use PV=nRT and substitute (PV) in for (nRT) in the equation: w=-nRT In(V2/V1) ?
Yes
If so, what should I use for values of P and V? Final/Initial/delta?
How does PV in the initial state compare to PV in the final state?

IoFawkes
TSny said:
How does PV in the initial state compare to PV in the final state?
P1V1=P2V2 so it doesn't matter which I use as long as P and V are both initial values, or final values. Correct?
EDIT: Except it's asking for work done, so would it be the Change in Pressure and Volume?
Io

Last edited:
IoFawkes said:
P1V1=P2V2 so it doesn't matter which I use as long as P and V are both initial values, or final values. Correct?
Yes
EDIT: Except it's asking for work done, so would it be the Change in Pressure and Volume?
nRT is a constant for an isothermal process. At any point along the process, nRT has the same value. The ideal gas law tells us that for any state, nRT = PV. So, nRT for the isothermal process equals PV evaluated for any state along the isothermal process.

nRT would not correspond to a change in PV.

IoFawkes
TSny said:
nRT is a constant for an isothermal process. At any point along the process, nRT has the same value. The ideal gas law tells us that for any state, nRT = PV. So, nRT for the isothermal process equals PV evaluated for any state along the isothermal process.

nRT would not correspond to a change in PV.

Ah, that makes sense, thanks! How wonderful a change in perspective.

Io

## 1. What is work (w) in the context of isothermal gas expansion/compression?

In this context, work (w) refers to the amount of energy required or released during the expansion or compression of a gas at a constant temperature.

## 2. How do you calculate work (w) for isothermal gas expansion?

The formula for calculating work (w) for isothermal gas expansion is w = nRTln(V2/V1), where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, V2 is the final volume, and V1 is the initial volume.

## 3. How do you calculate work (w) for isothermal gas compression?

The formula for calculating work (w) for isothermal gas compression is w = -nRTln(V2/V1), where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, V2 is the final volume, and V1 is the initial volume. The negative sign indicates that work is being done on the gas rather than being released.

## 4. What is the unit of measurement for work (w) in isothermal gas expansion/compression?

The unit of measurement for work (w) in isothermal gas expansion/compression is joules (J). This is the standard unit of measurement for energy.

## 5. What is the significance of calculating work (w) for isothermal gas expansion/compression?

Calculating work (w) for isothermal gas expansion/compression is important in understanding the energy changes in a system. It can also be used to determine the efficiency of a process and can be applied in various fields such as thermodynamics, chemistry, and engineering.

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