AE 223 - Thermodynamics and Propulsion
Tutorial - 1: First law of thermodynamics
Monday 30th July, 2018
(Please follow sign conventions and notations as used in lectures.)
1. Can we estimate the kinetic energy of the gas in the cylinder in problem Example 4.1, knowing the
rpm of the engine to be 3000, such that the compression stroke is completed in 14 ms. Compare the
changes in kinetic energy over the compression stroke to the change in temperature and pressure,
to see if they are negligible. Take the compression ratio to be 5, such that the volume of the gas
is reduced by a factor of 5 during the compression stroke and the processes can be assumed to be
adiabatic.
2. In a piston-cylinder arrangement, 0.02 m3 of nitrogen gas is compressed reversibly and isothermally from initial pressure of 2.05 bar to 4.2 bar. The initial temperature is 250 C inside the cylinder.
Calculate the work done and heat transfer during the process.
3. A cylinder fitted with a heavy piston has air at 101.325 kPa and 325 K. The piston rests on a step
such that the initial volume of the air in the cylinder is 0.05 m3 . The mass of the pistons is 3 kg
and area is 0.1 m2 . Heat is supplied to the cylinder such that the pressure inside rises. At some
point, the pressure is high enough to lift the piston to the next step at 1 m. Calculate the work done
by the air and the heat transferred to the cylinder. Also show the process on the p − V diagram.
4. Let us consider the power stroke of an internal combustion engine, where heat is added to the
compressed gas at 1500 kPa and initial volume 300 cm3 . The piston moves out of the cylinder as
the gas expands to ten times the initial volume. During this process, the gas does work against the
inertia of the crank shaft mechanism, which is modeled as an opposing force of the form F = 10x,
where x is the piston displacement in m and F is in kN. Calculate the final pressure of the gas and
the work done by the gas. Also draw the p-V diagram of the expansion process. Take the diameter
of the piston as 30 cm.