Assignment1 MEL140 - 2013.pdf

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Department of Mechanical Engineering, IIT Delhi

MEL 140 Engineering Thermodynamics

Assignment 1

1. A piston encloses a gas within a cylinder and is restrained by a linear spring as shown in Fig.1.

The initial pressure and the volume of the gases are 150kPa and 0.001m3, respectively. The

spring touches the piston but exerts no force at the initial position. The gas is heated until the

volume is tripled and pressure is 1000kPa. (a)Draw the p-V diagram for the process (b)

calculate the work done by the gas (c) What is the work done against the piston and spring?

Fig.1

2. During the expansion of the gas in a cylinder – piston system, these data were taken:

Pressure, kPa Volume, m3

10 1

4.06 2

2.39 3

1.65 4

1.23 5

0.974 6

0.797 7

0.669 8

0.575 9

0.501 10

Find the work done during the process.

3. Calculate the work required to stretch an unstressed steel wire from 1 to 1.001m. Young’s

modulus, E is 21011

N/m2 and the cross sectional area, A is 310

-6m

2.

4. An automotive battery is charged with a battery charger. The charger operates for 1 hour at

12V and a current of 25A. Calculate work done on the battery.

5. Show that the minimum work required to produce a spherical soap bubble of diameter, d is

2d2.

6. A 4m5m7m room is heated by the radiator of the steam heating system. The steam radiator

transfers heat at a rate of 10,000 kJ/hour and a 100W fan is used to distribute the warm air in

the room. The rate of heat loss from the room is estimated to be about 5000kJ/hour. If the

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initial temperature of the room is 10oC, determine how long it will take for the air temperature

to rise to 20oC. Assume constant specific heats at room temperature. Refer Fig.2.

Fig.2

7. An insulated cylinder is divided into two parts of 1m3 each by an initially locked piston as

shown in Fig.3. Side A has air at 200kPa, 300K, and side B has air at 1.0MPa, 1000K. The

piston is now unlocked so that it is free to move, and it conducts heat so that the air comes to a

uniform temperature TA = TB. Find the mass in both A and B and the final temperature, T and

final pressure, P.

Fig.3

8. Two tanks are connected by a valve as shown in Fig.4. One tank contains 2 kg of carbon

monoxide gas at 77oC and 0.7 bar. The other tank holds 8 kg of the same gas at 27

oC and 1.2

bar. The valve is opened and the gases are allowed to mix while receiving energy by heat

transfer from the surroundings. The final equilibrium temperature is 42oC. Using the ideal gas

model, determine (a) the final equilibrium pressure, in bar (b) the heat transfer for the process,

in kJ.

Fig.4

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9. A balloon is filled with helium. The initial diameter of the balloon is Db,1 = 8 cm. The initial

temperature of the helium in the balloon is T1 = 20◦C. The balloon is surrounded by air at

pressure Patm = 1 atm. The balloon is a thin film with surface tension that depends on the

diameter according to: , where K = 5.2 × 10

4 N/m

3. The helium within the balloon is

heated until the balloon diameter is Db,2 = 9 cm. (a)Determine the initial pressure in the balloon

and the mass of helium in the balloon. (b) What is the work done by the helium to the balloon

material during the heating process?

10. A 400 litre tank, A (Fig.5), contains argon gas at 250 kPa and 30oC. Cylinder B, having a

frictionless piston of such mass that a pressure of 150 kPa will float it, is initially empty. The

valve is opened and argon flows into B and eventually reaches a uniform state of 150 kPa and

30oC throughout. What is the work done by the argon?

Fig.5