Matter and Energy

Matter and EnergyThermodynamics - “the study of systems and energy

transfer”

On a day in January, a household digital thermometer gives a reading of 30oC; what is the absolute temperature outside?

Known: A thermometer reads 30oCFind: Absolute temperature read by thermometer [K]

Sketch:

Assumptions: N/A

Solution:273.1 T(C) T(K)

273.1 30 T(K)

K 303.1 T(K)

Matter and EnergyThermodynamics - “the study of systems and energy

transfer”A spherical balloon has a diameter of 3m. The air trapped inside has a specific volume of 0.94 m3/kg. Determine the weight of the air inside the balloon assuming the acceleration of gravity is 9.8 m/s2.

Known: A sphere is filled with air (D=3m, v = 0.94 m3/kg)Find: Weight of the air, [N]

Sketch:

Assumptions: Closed System, g = 9.8 m/s2

Solution:

D = 3m

3

3

3

m 14.14

)m 1.5(3

43

4

V

V

rV

m 1.52

m 32

r

Dr

kg 15.04

kg

3m0.94

3m 14.14

m

v

Vm

Vvmm

Vv

N 4.147 147.4Weight

)s

m kg)(9.8 (15.04Weight

mgWeight

2s

m-kg

2

mgWeight m

Vv 3

3

4rV

2

Dr

Matter and EnergyThermodynamics - “the study of systems and energy

transfer”A manometer filled with water is used to measure the pressure of a gas in a tank. The water (ρ = 990 kg/m3) is displaced by a height of 0.025 meter. What is the gage pressure of the gas in the tank? What is the absolute pressure?

Tank

Patm

Known: A water manometer measures gas pressure (ρ = 990 kg/m3), h = 0.025 m Find: Pressure of gas in tank, Ptank in Pa; Absolute pressure of gas in tank, Pabs in PaSketch:

Assumptions: Patm = 101.3 kPa, Ptank = P1 , g = 9.8 m/s2

Solution: Ptank = P1= ρghPtank = (990 kg/m3)(9.8 m/s2)(0.025m)Ptank = 242.6 Pa

Pabs = Ptank + Patm =. 2426 kPa + 101.3 kPa = 101.54 kPa

Matter and EnergyThermodynamics - “the study of systems and energy

transfer”A vertical piston-cylinder device (D = 10 cm) contains a trapped mixture of gases. The piston (m = 3 kg) falls and compresses the gas mixture from 4 m3 down to 1.2 m3. How much work is done by the piston on the gas mixture?Known: A gas mixture is compressed inside of a piston-cylinderFind: Work done by the piston, [kJ]

Sketch:

Assumptions: Closed System ,

Solution:

)V(V P Work 12 area

Force P mgWeight Force

2

D2 r ,πrArea In this case, the work is negative; that implies that this work is going into the system.

vertical piston-cylinder

Vertical-piston cylinder -> Isobaric

Matter and EnergyThermodynamics - “the study of systems and energy

transfer”A piston cylinder containing a gas is compressed. The work done on the system during compression is 60 kJ and the change in energy of the system is 300 kJ. Find the magnitude and direction of any heat transfer associated with this process.Known: A gas is compressed inside of a piston-cylinderFind: Q, [kJ]; Direction of heat transfer

Sketch:

Assumptions: Closed System

Solution:

2-12-12-1 W- Q E Q W E 2-12-12-1 Q kJ) (-60 kJ 003 2-1 Q kJ 402 2-1

The work is going into the system, so we must give it a negative sign…

The sign on the heat transfer is positive, so heat is flowing into the system.

Matter and Energy

Energy can go into or out of a system as either work or heat …so far we’ve covered:

Thermodynamics - “the study of systems and energy transfer”

Work:• Mechanical Work = F x d• Expansion/Compression Work =

isobaric if ,)( 12

2

1

VVPPdVV

V

Energy, (E):• Potential Energy (PE) = m g h• Kinetic Energy (KE) = • Internal Energy (U)

2

2

1mV

Heat:• Heat (Q)

} E = PE + KE

+ U

Matter & Energy Homework A spherical balloon has a diameter of 5m. The air trapped inside has a

specific volume of 0.84 m3/kg. Determine the weight of the air inside the balloon assuming the acceleration of gravity is 9.8 m/s2.

A manometer filled with water is used to measure the pressure of a gas in a tank. The water (ρ = 1000 kg/m3) is displaced by a height of 60 centimeter. What is the gage pressure of the gas in the tank? What is the absolute pressure?

A vertical piston-cylinder device (D = 30 cm) contains a trapped mixture of gases. The piston (m = 0.5 kg) falls and compresses the gas mixture from 4 m3 down to 1m3. How much work is done by the piston on the gas mixture?

A piston cylinder containing a gas is compressed. The work done by the system during expansion is 100 kJ and the change in energy of the system is 200 kJ. Find the magnitude and direction of any heat transfer associated with this process.