Calculating Workdone of a Compressed Diatomic Gas

[vijiraghs]

Homework Statement

A certain mass of a diatomic gas (gamma=1.4) occupies a volume of 100 cm^3 at a pressure of 75 cm of Hg. It is compreseed adiabatically until the pressure increases to 80 cm of Hg. Calculate the workdone in the process.

Homework Equations

W=1/(gamma -1)* (p1v1-p2v2)
=nR/(gamma-1)*(t1-t2)
where gamma=cp/cv
cp=molar specific heat of the gas at constant pressure
cv=molar specific heat of the gas at constant volume.

The Attempt at a Solution

i tried the formula and got -10 J but the correct answer is 29.2 J and i don't have a clue of the method.

 

[AvroArrow]

Could someone explain the method?The work done in the process is given by: W = 1/(γ - 1)*(p1*v1 - p2*v2) = 1/(1.4 - 1)*(75*100 - 80*100) = 29.2 J

 

[m2003]

I would first check to make sure that all the units are consistent and correct. In this case, it seems that the units for pressure are in centimeters of mercury (cm Hg), which should be converted to a standard unit of pressure such as Pascals (Pa). This could be causing the discrepancy in the calculated workdone.

I would also double check the values for the initial and final pressures and volumes to ensure they are accurate.

Additionally, it may be helpful to draw a diagram or use a graph to visualize the process and better understand the changes in pressure and volume.

Another approach could be to use the ideal gas law, PV=nRT, to calculate the change in temperature of the gas during the compression process. This can then be used in the equation W=nR/(gamma-1)*(t1-t2) to calculate the workdone.

Overall, it is important to carefully check all the variables and units, and to use the appropriate equations and methods to solve the problem accurately.