Question

Consider a piston-cylinder device with a piston surface area of 0.1 m^2 initially filled with 0.05 m^3 of saturated water vapor at the atmospheric pressure of 100 kPa. Now cold water is poured outside the cylinder, and the steam inside starts condensing as a result of heat transfer to the cooling water outside. If the piston is stuck at its initial position, determine the friction force acting on the piston and the amount of heat transfer when the temperature inside the cylinder drops to 30°C.

Answer 1

The friction force f = 10000 N

The heat transfer Q = 1.7936 KJ

Explanation:

Given data:

Surface area of Piston = 1 $m^{2}$

Volume of saturated water vapor = 100 K Pa

Steam volume = 0.05 $m^{3}$

Using the table of steam at 100 K pa

Steam density = 0.590 Kg/$m^{3}$

Specific heat $C_{p}$ = 2.0267 KJ/Kg K

Mass of vapor = S × V

m = 0.590 × 0.05

m = 0.0295 Kg

Solution:

a) The friction force is calculated

Friction force = In the given situation, the force need to stuck the piston.

= pressure inside the cylinder × piston area

= 100 × $10^{3}$  × 0.1

f = 10000 N

b)  To calculate heat transfer.

Heat transfer = Heat needs drop temperatures 30°C.

$Q=m c_{p} \ DT$

Q = 0.0295 × 2.0267 × $10^{3}$ × 30

Q = 1.7936 KJ