During some kind of process the pressure of 2 mol of nitrogen gas linearly depends on the volume:

p = p₀ + kV

here p₀ and k are constants. What are the values for these constants when the process is politropic?

3. In the industry enterprise we need to compress the volume of air (V₀) of the atmospheric pressure p₀  to the volume V₂. Initial temperature of the air is equal to the ambient temperature. We use two compressors to do this work. First compressor adiabatically compress the air to the volume V₁ (V₂<V₁< V₀), then the air is left to cool down isochorically to the ambient temperature and finally with the second compressor adiabatically compressed from the volume V₁ to the volume V₂. What should be V₁  to compress the air in the lowest work value? What is equal to that work? Is it worth to use two compressors, not one who can compress the air at once?

4. The vertical, long, impervious to heat cylinder (cross-section S) has lower end closed.  The piston (mass m) can move without friction in the cylinder. At first moment the piston is being held in height H above the cylinder bottom. Above the piston is vacuum and thereunder the piston is pressure p single-atom gas. The piston is being released. What will be the maximum speed the piston will reach? pS > mg,  the mass of the piston is much bigger than the mass of the gas.

5. The piston can move without friction in the cylinder. He is attached to the left wall with the spring of rigidity k (1 pic.). The spring wouldn't be warped if the piston was attached to the right wall. In the left side of the piston is vacuum, in the right side - neon, which has pressure p₀, temperature T₀ and volume V₀. What is the heat capacity of the system? We can ignore the heat capacity of the piston and the cylinder.