1. Ethane, initially at 35 kPa with a volume of .12 m³, is compressed without friction in a cylinder until its volume is halved in such a manner that its pressure and volume are linearly related, p = a + bV. The final pressure is 80 kPa and the change in internal energy of the ethane is 3.22 kJ. Determine the heat transfer. 2. Ethane in a closed system is compressed without friction from 95 to 190 kPa in such a manner that pV = constant. Initially, the density is 1.11 kg / m³ and the volume is 0.045 m³. During the compression, 2.96 kJ of heat is removed from the ethane. Determine the change in internal energy of the ethane. 3. A closed vertical cylinder containing 0.3 kg of nitrogen at 90ºC is fitted with a weighted, frictionless piston so that a constant pressure of 275 kPa is maintained on the gas. The nitrogen is stirred by a paddle wheel inserted through the cylinder wall until the absolute temperature of the gas is doubled. During the process, 20 kJ of heat is transferred from the nitrogen to the surroundings. Determine the amount of paddle-wheel work required for this process.