Exam 19: Work, heat, and the First Law of Thermodynamics

The figure shows a pV diagram for 0.95 mol of gas that undergoes the process 1 → 2.The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1.What is the final temperature of the gas? The ideal gas constant is R = 8.314 J/mol ∙ K = .

Betelgeuse is a red supergiant star in the constellation Orion.It radiates heat at the rate of 2.70 × 10³⁰ W and has a surface temperature of 3000 K.Assuming that it is a perfect emitter,what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

An ideal monatomic gas cools from 455.0 K to 405.0 K at constant volume as 831 J of energy is removed from it.How many moles of gas are in the sample? The ideal gas constant is R = 8.314 J/mol ∙ K.

A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact.The specific heat of aluminum is more than double that of copper.Which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium?

A block of ice at 0.000°C is added to a well-insulated 147-g aluminum calorimeter cup that holds 200 g of water at 10.0°C.The water and aluminum cup are in thermal equilibrium,and the specific heat of aluminum is 910 J/(kg ∙ K).If all but 2.00 g of ice melt,what was the original mass of the block of ice? The specific heat of water is 4190 J/(kg ∙ K),its latent heat of fusion is 334 kJ/kg,and its latent heat of vaporization is 2260 kJ/kg.

A cube at 100°C radiates heat at a rate of 80.0 J/s.If its surface temperature is increased to 200°C,the rate at which it will now radiate is closest to

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C.The specific heat of aluminum is 900 J/(kg ∙ K)and that of water is 4190 J/(kg ∙ K).What is the final temperature of the system,assuming no heat is exchanged with the surroundings?

The process shown in the pV diagram in the figure is

A monatomic ideal gas undergoes an isothermal expansion at 300 K,as the volume increased from to The final pressure of the gas is The ideal gas constant is R = 8.314 J/mol ∙ K.The change in the internal (thermal)energy of the gas is closest to

A substance has a melting point of 20°C and a heat of fusion of 3.9 × 10⁴ J/kg.The boiling point is and the heat of vaporization is 7.8 × 10⁴ J/kg at a pressure of 1.0 atm.The specific heats for the solid,liquid,and gaseous phases are 600 J/(kg∙K),1000 J/(kg∙K),and 400 J/(kg∙K),respectively.The quantity of heat required to raise the temperature of of the substance from to at a pressure of 1.0 atm,is closest to

It is necessary to determine the specific heat of an unknown object.The mass of the object is measured to be 199.0 g.It is determined experimentally that it takes 16.0 J to raise the temperature 10.0°C.Find the specific heat of the object.

An 80-g aluminum calorimeter contains 380 g of water at an equilibrium temperature of A piece of metal,initially at is added to the calorimeter.The final temperature at equilibrium is 32°C.Assume there is no external heat exchange.The specific heats of aluminum and water are 910 J/kg ∙ K and 4190 J/kg ∙ K,respectively.The specific heat of the metal is closest to

During an adiabatic process,an ideal gas does 25 J of work.What is the change in the internal (thermal)energy of the gas during this process?

A compression,at a constant pressure of 190 kPa,is performed on 5.0 moles of an ideal monatomic gas.The compression reduces the volume of the gas from to The ideal gas constant is R = 8.314 J/mol ∙ K. The work done by the gas is closest to

The pV diagram shown is for 7.50 moles of an ideal diatomic gas taken through a cycle from a to b to c.The ideal gas constant is R = 8.314 J/mol ∙ K. (a)What is the highest temperature reached by the gas during the cycle? (b)What net work does the gas do during the cycle? (c)How much heat is exchanged with the gas during part bc of the cycle? Does it enter or leave the gas? (d)What is the change in the internal (thermal)energy of the gas during part bc of the cycle? (e)What is the change in the internal (thermal)energy of the gas during the entire cycle?

An ideal gas with γ = 1.30 occupies 7.0 L at 300 K and 200 kPa pressure.It is compressed adiabatically to 1/7 of its original volume,then cooled at constant volume to 300 K,and finally allowed to expand isothermally to 7.0 L.How much work does the gas do during this process? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.