A sample of ideal gas is confined in a frictionless, perfectly sealing piston–cylinder assembly. The gas undergoes the following two-step, quasi-static sequence:
• State 1: pressure 1.00×105Pa, volume 1.50L, temperature T1 (unknown).
• Process 1 (1 → 2): The gas is compressed isothermally at temperature T1 until its volume is 0.750L (State 2).
• Process 2 (2 → 3): Starting from State 2, the gas is heated at constant pressure until its volume again reaches 1.50L (State 3). The temperature measured at State 3 is 620K.
Assume the amount of gas remains constant throughout the experiment and that the external pressure always equals the internal pressure during each process.
(a) Determine the pressure in State 2. Express your answer in pascals and justify the relationship you use.
(b) Using algebraic manipulation of the appropriate relationships, calculate the initial temperature T1 numerically. Show all steps clearly.
(c) Verify quantitatively that the ratio of the product of pressure and volume to absolute temperature, i.e., TPV, is the same in all three states, and explain the physical significance of this consistency in the context of your calculations.