Exam 20: The First Law of Thermodynamics

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In an isothermal process

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In which process will the internal energy of the system NOT change?

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A 5-gallon container of water (approximately 20 kg)having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg)of water having a temperature of 50°F.What is the final equilibrium temperature (in °C)of the mixture?

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The R value of fiberglass batting,3.5 inches thick,is 11 ft2⋅°F⋅h/BTU.What is the thermal conductivity (in BTU/ft⋅°F⋅s)?

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In an adiabatic free expansion

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Determine the heat capacity (in calories/°C)of a lake containing one million gallons (approximately 4 million kilograms)of water at 15°C.

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A 5-g coin is dropped from a 300-m building.If it reaches a terminal velocity of 45 m/s,and the rest of the energy is converted to heating the coin,what is the change in temperature (in °C)of the coin? (The specific heat of copper is 387 J/kg⋅°C. )

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How much heat (in kcal)must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅°C. )

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In an isovolumetric process

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An 8 000-kg aluminum flagpole 100-m long is heated by the sun from a temperature of 10°C to 20°C.Find the work done (in J)by the aluminum if the linear expansion coefficient is 24 × 10−6 (°C)−1.(The density of aluminum is 2.7 × 103 kg/m3 and 1 atm = 1.0 × 105 N/m2. )

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The R-value of an insulating material is the thickness of the material divided by its thermal conductivity.When an insulating material consists of three layers with R-values R1,R2 and R3,the overall R-value of the insulation is given by

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How much water at 20°C is needed to melt 1 kilogram of solid mercury at its melting point of −39°C? (The heat of fusion of mercury is 2.8 cal/gram).

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In braking an automobile,the friction between the brake drums and brake shoes converts the car's kinetic energy into heat.If a 1 500-kg automobile traveling at 30 m/s brakes to a halt,how much does the temperature rise in each of the four 8.0-kg brake drums? (The specific heat of each iron brake drum is 448 J/kg⋅°C).

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Water at room temperature,20°C,is pumped into a reactor core where it is converted to steam at 200°C.How much heat (in J)is transferred to each kilogram of water in this process? (csteam = 2 010 J/kg⋅°C;Lsteam = 2.26 × 103 J/g;1 cal = 4.186 J. )

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A wall is constructed of a 2 inch layer of fiberglass board (R = 8)and six inches of fiberglass batting (R = 19).If the temperature on the outside surface of the fiberglass board is 50°F and the temperature on the inside surface of the fiberglass batting is 68°F,what is the temperature (in °F)at the interface? (The units of R are ft2⋅°F⋅h/BTU. )

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Determine the work done by 5 moles of an ideal gas that is kept at 100°C in an expansion from 1 liter to 5 liters.

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How much heat (in kilocalories)is needed to convert 1.00 kg of ice at 0°C into steam at 100°C?

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A cup of coffee is enclosed on all sides in an insulated container 1/2 cm thick in the shape of a cube 10 cm on a side.The temperature of the coffee is 95°C,and the temperature of the surroundings is 21°C.Find the rate of heat loss (in J/s)due to conduction if the thermal conductivity of the cup is 2 × 10−4 cal/s⋅cm⋅°C.

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Gas in a container increases its pressure from 1 atm to 3 atm while keeping its volume constant.Find the work done (in J)by the gas if the volume is 5 liters.

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A gas expands from A to B as shown in the graph.Calculate the work (in joules)done by the gas.(1 atm= 1.01 × 105 N/m2. ) A gas expands from A to B as shown in the graph.Calculate the work (in joules)done by the gas.(1 atm= 1.01 × 10<sup>5</sup> N/m<sup>2</sup>. )

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