Thermodynamics - internal energy change question

[chriswilson]

Homework Statement

Assume ideal gas conditions. Cp=(7/2)R, Cv=(5/2)R

15 moles of airis contained in a cylinder and prevented from escaping by a frictionless piston
initial conditions are 1.5 bar, gas volume 0.2m^3

final conditions required are 10 bar t 27 degrees celsius

calculate the internal energy change and associated heat, Q, and work W, for
i) constant pressure process, followed by constant volume process
ii) constant volume process followed by constant pressure process

Homework Equations

the ideal gas law pV=nRT i assume can be used to find the temperature at the initial temperature.

The Attempt at a Solution

once I've found deltaU i think I could work out the heat and work but I really don't know how to get started. my textbook gives equations of

deltaU= integral(CvdT) however I'm not really sure how to use this.

sorry if its not too clear I hope you can understand it.

 

[xiaoB]

Homework Statement

Assume ideal gas conditions. Cp=(7/2)R, Cv=(5/2)R

15 moles of airis contained in a cylinder and prevented from escaping by a frictionless piston
initial conditions are 1.5 bar, gas volume 0.2m^3

final conditions required are 10 bar t 27 degrees celsius

calculate the internal energy change and associated heat, Q, and work W, for
i) constant pressure process, followed by constant volume process
ii) constant volume process followed by constant pressure process

Homework Equations

the ideal gas law pV=nRT i assume can be used to find the temperature at the initial temperature.

The Attempt at a Solution

once I've found deltaU i think I could work out the heat and work but I really don't know how to get started. my textbook gives equations of

deltaU= integral(CvdT) however I'm not really sure how to use this.

sorry if its not too clear I hope you can understand it.

I don't know these for you is useful or not ?

(1)For constant pressure process :Amount of heat entering the gas is dQ=nC_pdT;We just express dW in terms of the temperature change dT is dW=pdV=nRdT.Therefore,first law,dQ=dU+dW => nC_pdT=dU+nRdT.

(2)For constant volume process: The pressure increases during this process, but the gas does not work (dW=0) because the volume is constant. Therefore, first law: dQ=dU+dW => dQ=dU=nC_vdT.Is same(deltaU= integral(CvdT)).

Here i should inform you that what i wrote was no going details. So, you should read more out from the books.

 

[Andrew Mason]

Homework Statement

Assume ideal gas conditions. Cp=(7/2)R, Cv=(5/2)R

15 moles of airis contained in a cylinder and prevented from escaping by a frictionless piston
initial conditions are 1.5 bar, gas volume 0.2m^3

final conditions required are 10 bar t 27 degrees celsius

calculate the internal energy change and associated heat, Q, and work W, for
i) constant pressure process, followed by constant volume process
ii) constant volume process followed by constant pressure process

1. find the initial temperature.

2. find the final volume. Is the process from initial to final condition a compression or expansion?

3. draw PV diagram and plot the beginning and end points.

4. i) from the initial point, draw a constant pressure path followed by a constant volume path to reach the end point.

4 ii) from the initial point, draw a constant volume path followed by a constant pressure path to reach the end point.

5. use Cp and Cv to determine the Q for each part of the path and apply the first law to determine the change in internal energy and work done.

AM