Problem # p024

Ideal Gas and Work

An ideal gas with a specific gas constant R=0.29 kJ/(kg K) is compressed from an initial state, p1 = 0.1 MPa v1=1 m3/kg, to a pressure p2= 1 MPa.
During the compression, including the initial state, index 1, and the end state, index 2, pressure and specific volume are related according to :

p v1.2 = constant

  1. What is the value of the initial temperature, T1 ?
  2. What is the specific volume, v2, at the end of the compression ?
  3. What is the temperature, T2, at the end of the compression ?
  4. Derive the equation for the amount of work which has to be done to compress 1 kg of the gas from the initial state 1 to the end state 2. Start with the definition of work :

  5. Evaluate the equation obtained under 4) using the numbers you obtained previously.