Question

Heat is applied to a rigid tank containing water initially at 200C, with a quality of 0.25, until the pressure reaches 8 MPa. Determine the amount of heat added. Draw this process on a T-v diagram with respect to the saturation curve. For full credit this sketch of the process must accurately represent the process

Answer 1

Answer:1747.53KJ/kg

Explanation:

Given data

Initial Temprature$\left ( T_i\right )=200^{\circ}$

Quality$\left ( \chi\right )=0.25$

Final pressure$\left ( P_2\right )=8MPa$

Given tank is rigid therefore specific Volume remains same

now calculating properties at $200^{\circ}$

$\nu _f=0.001156m^3/kg$

$\nu {fg}=0.126434m^3/kg$

$h_f=852.26KJ/kg$

$h_{fg}=1939.8KJ/kg$

Now Specific volume of steam at $200^{\circ}$

$\nu _1=\nu _f+\chi \times \nu {fg}$

$\nu _1=0.001156+0.25\times 0.126434$

$\nu _1=0.03276m^3/kg$

$h_1=h_f+\chi \times h_{fg}$

$h_1=852.26+0.25\times 1939.8$

$h_1=1337.21 KJ/kg$

Now $\nu_1=\nu_2$

$0.03276=\nu_2$

At 8 MPa and $\nu =0.03276m^3/kg$

$\nu _g=0.02356$

Since $\nu _2\ is\ greater\ than \nu _g$

therefore final state of steam is superheated at $T=381^{\circ}$

at this state $h_2=3084.74 KJ/kg$(obtained from steam table)

Therefore heat added

$Q=h_2-h_1=3084.74-1337.21=1747.53 KJ/kg$