Thermal Physics - Calculating Work, Heat, and Internal Energy in a Gas Cylinder

[Niles]

Homework Statement

A cylinder contains one litre of air at T = 300 K and P = 105
Pa. At one end of the cylinder is a massless piston, whose
surface area is 0.01 m^2. Suppose you push the piston in
suddenly, with a force of 2000 N. The piston moves only 1
mm, before being stopped by an immovable barrier.
(a) How much work have you done on the system?

(b) How much heat has been added to the gas?

(c) Assuming that all the energy added goes to the gas,
how much does the internal energy of the gas increase?

(d) Use the thermodynamic identity (dU = T dS −
PdV ) to calculate the change in entropy of the gas
(once it is back in equilibrium).

The Attempt at a Solution

a) The work done is simply: W = F*d - and the work done is positive.

b) No heat is being added, right? So the internal energy is just equal the work done one the gas, and the temperature rises. Can you confirm this statement?

c) We have (considering that b is correct) that dU = W.

d) Here I am a little lost. Can I calculate the entropy when dU = 0 and then when dU != 0 and then add them?

 

[CFDFEAGURU]

Check the Ideal Gas Properties of Air table in any thermodynamic text. That should point you in the right direction.