Final answer:
The work done on the gas is 22.5 lbf.ft and there is no heat transfer in this process.
Step-by-step explanation:
In this problem, we are given the initial pressure and volume of air in a piston-cylinder assembly, and we need to determine the work and heat transfer when the volume of the air is doubled at constant pressure. Since the air is heated at constant pressure, this process is described as an isobaric process. In an isobaric process, the work done by the gas is given by the formula:
Work = Pressure × Change in Volume
The initial pressure is given as 30 lbf/in2 and the initial volume is given as 0.75 ft3. The final volume is twice the initial volume, which is 2 × 0.75 ft3 = 1.5 ft3. Therefore, the change in volume is 1.5 ft3 - 0.75 ft3 = 0.75 ft3. Substituting these values into the formula, we can calculate the work as:
Work = 30 lbf/in2 × 0.75 ft3 = 22.5 lbf.ft
Now, to calculate the heat transfer, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Since the process is adiabatic and no heat is transferred, the change in internal energy is equal to the work done by the system. Therefore, the heat transfer is zero.