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

Step-by-step 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)`

`\\u _f=0.001156m^3/kg`

`\\u {fg}=0.126434m^3/kg`

`h_f=852.26KJ/kg`

`h_(fg)=1939.8KJ/kg`

Now Specific volume of steam at
`200^(\circ)`

`\\u _1=\\u _f+\chi * \\u {fg}`

`\\u _1=0.001156+0.25* 0.126434`

`\\u _1=0.03276m^3/kg`

`h_1=h_f+\chi * h_(fg)`

`h_1=852.26+0.25* 1939.8`

`h_1=1337.21 KJ/kg`

Now
`\\u_1=\\u_2`

`0.03276=\\u_2`

At 8 MPa and
`\\u =0.03276m^3/kg`

`\\u _g=0.02356`

Since
`\\u _2\ is\ greater\ than \\u _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`