Old spec Tutorial 1 Problem 3 (ENGR5003)

Old spec Tutorial 1 Problem 3TutorialOld spec ENGR2172:210 min

ENGR217 (old spec) Thermo L6 Tutorial 1, Problem 3 official answers

1 kg of air at an absolute pressure $p_1 = 2$ bar and temperature $T_1 = 300$ K is isothermally compressed in a cylinder to half its original volume ( $R_g = 0.287$ kJ/(kg K)).

Formulas you may need

Isothermal ideal gas work: $W = mR_gT\ln\dfrac{V_2}{V_1}$ (work done by the gas) (on the formula sheet)
First law (closed system) $\Delta U = Q - W$ ; isothermal ideal gas $\Delta U = 0$ (on the formula sheet)
Ideal gas $pV = mR_gT$ (on the formula sheet)
Work done by the atmosphere on the outside of the piston $W_{atm} = p_0\,|\Delta V|$ (learn this)

(a)
Calculate the work done on the air and the heat transfer from the air.
work done on the air =kJ
heat rejected by the air =kJ
(b)
What is the net work needed to compress the air if the atmospheric pressure is 1 bar?
work done by the atmosphere =kJ
net work needed =kJ