A cube of aluminium measures 1 m along each side. In the centre of the cube there is a small spherical cavity with a diameter of 1 cm. When the cube is heated from 10 ◦C to 30 ◦C, what is the percentage increase in the volume of the central cavity? (The lin- ear thermal expansion coefficient of aluminium is 23 × 10−6 K−1 .) 0.14%

Air initially at 0.75 bar, 1000 k, and occupying a volume of 0.12 m^3 undergoes two processes. process 1-2: the air is compressed isothermally until the volume is halved. process 2-3: the air undergoes a constant pressure process until the volume is halved again. assume ideal gas behavior. a) determine the mass of the air, in kg. b) the work and the heat transfer for each of the two processes, in kj. (100 kj = 1 bar . m^3)