Thermodynamics 1 - Tutorial 1
Gas Law, Work Transfer, Heat Transfer, 1st Law for Closed Systems,
the Adiabatic Process
Ro = 8.314 J/mol.K, Cv air=718 J/kgk, Rair = 287 J/kg.K, MH2 = 2 g/mol, MH2O =18 g/mol
Note: Final answers for every question are given in square brackets.
1. Using the information given above calculate:
a) The mass of hydrogen in a 11m3 tank at 75 bar, 350 K
[56.7 kg]
[101.8 bar]
b) If the tank is now heated to 475 K, find the new pressure
c) If steam can be regarded as a perfect gas, find the volume needed to contain 11g at 3 bar,
310K
[5.25 L]
2. 200g of pure hydrogen at 273 K is compressed isothermally from 1.013 bar to 10.13 bar.
Calculate the work transfer.
[-522.6 KJ]
ππ
ππ
πΎπΎ
3. A perfect gas, when compressed or expanded, follows a process described by ππ1 = οΏ½ππ2 οΏ½ where
2
1
γ (specific heat ratio) is dependant on the gas. Using the 1st Law of thermodynamics show that the
ππ ππ2 −ππ1 ππ1
work transfer in such a process is given by π€π€ = 2 1−πΎπΎ
. Then, if the gas is air with γ = 1.4 and
is compressed adiabatically from 1.25 bar, 270K, 0.6m3 to 5 bar.
Calculate:
a) The mass, the final volume, and the final temperature
b) The work transfer, including the sign.
[0.968 kg, 0.223 m3,401.3 K]
[-91.25 KJ]
c) The power required if the process is performed 670 times per min
[1018.96 kW]
4. Figure 1 below shows a 150 mm diameter piston weighing 310kg which slides in a frictionless
cylinder. The piston rests on a 200 mm long pin and traps air below it at 300K, 1.013bar. At the
top of the cylinder, 300 mm above the piston, is a collar that prevents the piston from being pushed
out of the cylinder. The air outside the cylinder is at 1.013 bar. If the air below the piston is
continuously heated, calculate:
a) The air temperature when the piston first lifts off the pin.
[809.4 K]
b) The air temperature when the piston first reaches the collar
[2023.5 K]
c) The pressure when the temperature reaches 2700 K.
[3.65 bar]
d) The work done by the air.
[1449 J]
e) The increase in potential energy of the piston
[912 J]
f) The heat transfer for part (a)
[1521.5 J]
g) The heat transfer from pin lift-off to when the pin just reaches the collar. [5075 J]
h) Why is the work done by the air not equal to the change in potential energy of the piston?
atm @ 1.013 bar
300 mm
310 kg
air
300 K
1.013 bar
Figure 1
200 mm
0
