#### Polytropic Process, Heat + Work

A cylinder closed off by a movable piston contains propane gas
at 100 kPa and 300 K
occupying initially a volume of 100 ltr ( 1 m³ = 1000 ltr ). The gas is
now slowly compressed
according to the relation :

p V^{1.2} = constant
until the pressure reaches 400 kPa. Assume that propane behaves like an
ideal gas of molecular weight M=44.1 kg/kmol. (Universal gas
constant is 8.3144 kJ/(kmol K) ).

- How many kilogram of propane are inside the cylinder ?

- What is the volume the gas occupies after the compression ?

- What is the final temperature ?

- How much work is being done during the compression ?

- How much heat is added (removed) during the process ?
Assume that the internal energy needed to bring propane from a state
1 to a second state 2 can be calculated according to :

u_{2} - u_{1} = c_{v} (
T_{2} - T_{1} ) with
c_{v} = 1.49 kJ/(kg K)