A frictionless piston-cylinder device contains 5 kg of nitrogen at 100 kPa and 250 K. Nitrogen is now compressed slowly according to the relation PV1.4= constant until it reaches a final temperature of 450 K. Calculate the work input during this process.

Question

Anot1954 · Accepted Answer

W=mR(T2−T1)1−n&amp;nbsp;=5⋅0.2968⋅(450−250)1−1.4kJ&amp;nbsp;=-742kJ Result&amp;nbsp;W=−742kJ

Andre BalkonE · Accepted Answer

Step 1:Given:The ideal gas law states:PV=nRTWhere:P = pressureV = volumen = number of moles of gasR = gas constantT = temperatureFirst, let&#039;s find the initial volume of the nitrogen gas. Since the piston-cylinder device is frictionless, the volume remains constant throughout the process. We can rearrange the ideal gas law to solve for volume:V=nRTPSubstituting the given values:V1=(5kg)·(8.314J/mol·K)·(250K)100kPa=10435.5100=104.36m3Step 2:Now, let&#039;s find the final volume of the nitrogen gas. Using the given relation PV1.4=constant, we can express volume in terms of pressure:V=(constantP)11.4Since the process is slow and quasi-static, the constant remains the same. We can use the initial pressure and volume to find the constant:PV1.4=constant=P1V11.4=(100kPa)·(104.36m3)1.4Now, using the final temperature of 450 K, we can find the final pressure:P2V21.4=P1V11.4P2=P1V11.4V21.4Substituting the given values:P2=(100kPa)·(104.36m3)1.4V21.4Now, let&#039;s find the final volume using the ideal gas law:V2=nRT2P2Substituting the given values and solving for V2:V2=(5kg)·(8.314J/mol·K)·(450K)P2Step 3:Now, we can calculate the work done during the process using the equation:W=∫V1V2PdVSince the process is quasi-static, we can replace P with nRTV:W=∫V1V2nRTVdVIntegrating the equation and solving for W:W=nRTln(V2V1)Substituting the given values and solving for W:W=(5kg)·(8.314J/mol·K)·450K·ln(V2V1)Now, we can substitute the expressions for V1, V2, and solve for W.

Jazz Frenia · Accepted Answer

The ideal gas law states: PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.The work formula for a polytropic process is: W=P2V2−P1V11−n, where W is the work, P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and n is the polytropic index.Given:Initial pressure, P1=100kPaInitial temperature, T1=250KFinal temperature, T2=450KPolytropic index, n=1.4Mass of nitrogen, m=5kgFirst, we need to find the initial volume using the ideal gas law. Rearranging the equation, we have:V1=nRT1P1Substituting the known values, we get:V1=(m/M)RT1P1where M is the molar mass of nitrogen.Next, we find the final volume using the ideal gas law and the given final temperature, T2:V2=(m/M)RT2P2Finally, we can calculate the work input using the work formula for a polytropic process:W=P2V2−P1V11−nSubstituting the values of P1, P2, V1, V2, and n, we can solve for W.Note: The molar mass of nitrogen is approximately M=28.0134g/mol.

A frictionless piston-cylinder device contains 5 kg of nitrogen at 100 kPa and 2

Answered question

Answer & Explanation

New Questions in Other