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TERMODINAMIKA TEKNIK KIMIA IContoh-contoh SoalDisusun oleh :Yelmida AA U-tube mercury manometer with one arm open to atmosphere is used to measure pressure in a steam pipe. The level of mercury in open arm is 97.5 mm greater than that in the arm connected to the pipe. Some of steam in the pipe condenses in the manometer arm connected to the pipe. The height of this column is 34 mm. The atmospheric pressure is 760 mm of Hg. Find the absolute pressure of steam.Solution.

The specific heat capacity of the system during a certain process is given by : If the mass of the gas is 6 kg and its temperature changes from 25C to 125C find : a. Heat transferred b. Mean specific heat of the gas.Solution. Mass of the gas, m = 6 kg. Change in temperature of the gas = 25C to 125C

(b) Mean specific heat of the gas, cn:(a) Heat transferred, Q :A cylinder contains 1 kg of a certain fluid at an initial pressure of 20 bar. The fluid is allowed to expand reversibly behind a piston according to a law pV2 = C until the volume is doubled. The fluid is then cooled reversibly at constant pressure until the piston regains its original position ; heat is then supplied reversibly with the piston firmly locked in position until the pressure rises to the original value of 20 bar. Calculate the net work done by the fluid, for an initial volume of 0.05 m3

Solution.Mass of fluid

Considering of the process 1-2, v2 = 2v1

Work done by the fluid from 1 to 2 = Area 12 ML1

0.3 kg of nitrogen gas at 100 kPa and 40C is contained in a cylinder. The piston is moved compressing nitrogen until the pressure becomes 1 MPa and temperature becomes 160C. The work done during the process is 30 kJ. Calculate the heat transferred from the nitrogen to the surroundings.Cv for N2= 0.75 kJ/kg K.Solution. Mass of nitrogen, m = 0.3 kgTemperature before compression = 40C or 313 KTemperature after compression = 160C or 433 KThe work done during the compression process, W = 30 kJAccording to first law of thermodynamics :

Hence, heat rejected during the process = 3 kJ. A closed system of constant volume experiences a temperature rise of 25C when a certain process occurs. The heat transferred in the process is 30 kJ. The specific heat at constant volume for the pure substance comprising the system is 1.2 kJ/kgC, and the system contains 2.5 kg of this substance. Determine: (i)The change in internal energy ; (ii)The work done

Solution.Temperature rise, (T2 T1) = 25CThe heat transferred in the process, Q = 30 kJSpecific heat at constant volume, Cv = 1.2 kJ/kgCMass of the substance, m= 2.5 kg

A fluid system, contained in a piston and cylinder machine, passes through a complete cycle of four processes. The sum of all heat transferred during a cycle is 340 kJ. The system completes 200 cycles per min. Complete the following table showing the method for each item, and compute the net rate of work output in kW.

Solution. Sum of all heat transferred during the cycle = 340 kJ.Number of cycles completed by the system = 200 cycles/min.

The system completes 200 cycles/minNow, dE = 0, since cyclic integral of any property is zero.

The completed table is given below :

SinceA closed, rigid tank filled with water vapor, initially at 20 MPa, 520C, is cooled until its temperature reaches 400C. Using the compressibility chart, determinethe specific volume of the water vapor in m3/kg at the initial state.the pressure in MPa at the final state.

SOLUTIONKnown: Water vapor is cooled at constant volume from 20 MPa, 520C to 400C.Find : Use the compressibility chart to determine the specific volume and final pressure and compare the results.(a) From Table Critical Constants :

Since Z = pv/RT, the specific volume at state 1 can be determined as follows:

With these values for the tr and pr , the value of Z obtained from Compressibility chart approximately : 0.83

At state 2 : Since both mass and volume remain constant, the water vapor cools at constant specific volume, and thus at constant vR. Using the value for specific volume determined in part (a), the constant vR value is :Locating the point on the compressibility chart where :

the corresponding value for pR is about : 0.69.

Analyzing Polytropic Processes of Air as an Ideal GasAir undergoes a polytropic compression in a pistoncylinder assembly from p1=1 atm, T1= 70oF to p2=5 atm. Employing the ideal gas model with constant specific heat ratio k, determine the work and heat transfer per unit mass, in Btu/lb, if (a) n = 1.3, (b) n = k. Evaluate k at T1SOLUTIONKnown: Air undergoes a polytropic compression process from a given initial state to a specified final pressure.Find: Determine the work and heat transfer, each in Btu/lb.Schematic and Given Data:

Analysis : The work can be evaluated in this case from the expression

The heat transfer can be evaluated from an energy balance. Thus

when the specific heat ratio k is constant, cv is constant. Thus

or(....... a )(....... b)(a) For n = 1.3, the temperature at the final state, T2, can be evaluated from :

Using (a), the work is then

At 70 oF, k= 1.401 and cv = 0.171 BTU/lb.oR . Alternatively, cv can be found using :(....... C )

That is, no heat transfer occurs in the polytropic process of an ideal gas for which n = k.. Substituting values into Eq.(b),