quiz1_07_solution - MECH 310 Thermodynamics I American...

MECH 310 Thermodynamics I November 20, 2007
American University of Beirut, Fall 2007 Handout # Quiz 1 Solution
Quiz 1 Solution
Problem 1 (25 points)
Two kilograms of water are contained within a piston-cylinder arrangement. The piston
is weightless and undergoes frictionless motion. See Figure 1. At the initial state, there
are equal masses of liquid and vapor initially. The system is (process 1) slowly heated to
a position where the piston is locked, and then (process 2) the system is cooled to the
saturated vapor state at 50 ◦ C. The atmospheric pressure is p
a
= 101 . 4 kPa.
(a) Is process 1 isothermal, isobaric, or isochoric? Why? What about process 2? why?
(b) Draw the processes on a p - v diagram, and
H
2
O
H
2
O vacuum
partition
H
2
O
p
a
p
a
Figure 1: Schematic for problem 1.
Solution
(a) Process 1 is isobaric since force balance on the piston yields p = p
a
, where piston
inertia is neglected due to the slow heat addition. Process 2 is isochoric since both mass
and volume are fixed during this process.
(b) See Figure 2.
(c) State 1 corresponds to saturated mixture at p = p
a
, so that T
1
= 100 ◦ C. Noting that
x
1
= 0 . 5, then v
1
= v
f
( p
1
) + x
1
( v
g
( p
1
) - v
f
( p
2
)) = 0 . 0010435 + 0 . 5(1 . 673 - 0 . 0010435) =
0 . 837 m
3
/kg. The volume at state 1 is therefore