Question

Consider a steam radiator used to heat a room. The radiator is filled with superheated steam at 200 kPa and 200°C. At this moment both the inlet and outlet valves to the radiator are closed. Some time later the pressure of the steam is observed to drop to 100 kPa due to the heat transfer from the radiator to the room. a) Draw a diagram representing the process showing the initial and final states of the system. b) Sketch this process on a T-v (temperature-specific volume) diagram with respect to the saturation lines, critical point, and relevant constant pressure lines, clearly indicating the initial and final states. c) Using steam tables determine the specific volume of the steam. d) Using steam tables determine the final temperature and quality of the steam (if relevant)

Answer 1

v1 =1.0852 m^3/kg

T2=99.60°C

x(2)=64%

Step-by-step explanation:

For the initial condition we have superheated steam at 200kPa and 200°C from the thermodynamics tables we get the specific volume for this condition

`v=1.0852(m^(3))/(kg)`

We can locate this point in the T-v diagram (see picture) point 1.

Since both the outlet and inlet valve are closed, we can assume that the volume in the system is constant during the process.

For the second condition we know the pressure (100 KPa) and the specific volume (1.0852 m^3/kg) because this is constant.

The conditions for saturation at 100 KPa are:

`T^(sat)=99.60 C`

`v_(g)= 1.69402 (m^(3))/(kg)` specific volume for the saturated vapor.

`v_(f)= 0.00104315(m^(3))/(kg)` specific volume for the saturated liquid.

Since the specific volume for our condition is among the specific volume for saturated liquid and saturated vapor. We are in the saturated region, so the temperature for the final condition will be 99.60°C.

The quality (x) can be estimated considering that:

`v = (1-x)*v_(f) + x*v_(g)`

Clearing for x we have:

`x = ((v-v_(f)))/((v_(g)-v_(f)))`

So:

`x = ((1.0852 (m^(3))/(kg) - 0.00104315(m^(3))/(kg)))/(( 1.69402 (m^(3))/(kg) - 0.00104315(m^(3))/(kg)))= 0.64`

The quality is 64% in the final condition.