# Calculating value of R from P, V, T data and work done in compression process

• mh1985
In summary, the task is to calculate the value of R, specific gas constant for air, and the work done in an adiabatic compression process. This requires initial values for pressure, volume, and temperature, as well as the density of air. The mass of air in the tube can be calculated using the given density, but will change as the volume decreases. The adiabatic equation (PV^γ = c) can be used to calculate R, and then the work done can be determined from this value. Further clarification or assistance is needed for completing this task.
mh1985

## Homework Statement

Calculate a value of R, specific gas constant for air, from the values you have.

Also calculate the work done in the compression process.

## Homework Equations

Pv = RT

ρair = 1.2 kg/m^3

## The Attempt at a Solution

Have P,V and T data from an adiabatic compression. I think I need initial values for these but not sure what else.

Also we have been given the density for air so the mass of the air in the tube, m = ρ*V = 2.903172 x 10^-4 kg. However this will change surely as volume decreases?

Last edited:
I'm not sure how to use the data given to calculate R. Is there a way to use the adiabatic equation (PV^γ = c) to work it out? And then from this work out the work done in the compression process? Any help would be much appreciated. Thanks

## 1. How do you calculate the value of R from P, V, T data?

To calculate the value of R (the universal gas constant) from P (pressure), V (volume), and T (temperature) data, you can use the ideal gas law equation: PV = nRT. Rearrange the equation to solve for R: R = (PV)/(nT). Where n is the number of moles of the gas and T is in Kelvin.

## 2. What units should be used for P, V, and T when calculating R?

When using the ideal gas law equation to calculate R, P should be in units of pressure (such as atm or Pa), V should be in units of volume (such as liters or cubic meters), and T should be in units of temperature (such as Kelvin or Celsius). It is important to use consistent units for accurate results.

## 3. How can you determine the work done in a compression process?

The work done in a compression process can be calculated by using the equation W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. Make sure to use the correct units for P and ΔV (such as atm and liters) to get the work done in joules.

## 4. Can you calculate R using data from an isothermal compression process?

Yes, R can be calculated using data from an isothermal compression process. Since the temperature (T) remains constant in an isothermal process, the ideal gas law equation can be simplified to PV = nR. From this equation, R can be solved for as R = (PV)/(n). Make sure to use consistent units for accurate results.

## 5. How does the value of R differ for different gases?

The value of R is the same for all gases and is considered a universal constant. It is equal to 8.314 J/mol·K or 0.0821 L·atm/mol·K. However, the value of R may differ depending on the units used for pressure, volume, and temperature. For example, if pressure is given in atmospheres, the value of R will be different compared to using Pascals as the unit for pressure.

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