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

A 406.0 kg copper bar is put into a smelter for melting.The initial temperature of the copper is 300.0 K.How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg ∙ K,the heat of fusion for copper is 205 kJ/kg,and its melting point is 1357 K.)

A concrete wall of a cold storage room measures 3.0 m high,5.0 m wide,and 20 cm thick.The room temperature is maintained at -10°C and the outside temperature is 20°C The inside wall is to be covered by a layer of wood in order to reduce the rate of heat loss through the wall BY 90 percent.The thermal conductivities of concrete and wood are 0.80 W/m ∙ K and 0.040 W/m ∙ K,respectively.Under steady state conditions,the thickness of the layer of wood required is closest to

How much work is done by 3.00 mol of ideal gas when it triples its volume at a constant temperature of 127°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

A cylinder contains 1.2 moles of ideal gas,initially at a temperature of 116°C.The cylinder is provided with a frictionless piston,which maintains a constant pressure of on the gas.The gas is cooled until its temperature has decreased to 27°C.For the gas C_V = 11.65 J/mol · K,and the ideal gas constant R = 8.314 J/mol ∙ K. (a)Find the work done by (or on)the gas during this process.Is the work done by or on the gas? (b)What is the change in the internal (thermal)energy of the gas during this process? (c)How much heat is transferred to (or from)the gas during this process? Does this heat flow into or out of the gas?

The walls of an ice chest are made of 2.00-mm-thick insulation having a thermal conductivity 0.00300 W/m ∙ K.The total surface area of the ice chest is 1.20 m².If 4.00 kg of ice at 0.00°C are placed in the chest and the temperature of the outside surface of the chest is 20.0°C,how long does it take the ice to melt under steady state conditions? The latent heat of fusion of water is 79.6 cal/g = 334 kJ/kg.

A 200-g metal container,insulated on the outside,holds 100 g of water in thermal equilibrium at A 21-g ice cube,at the melting point,is dropped into the water,and when thermal equilibrium is reached the temperature is 15.00°C.Assume there is no heat exchange with the surroundings.For water,the specific heat is 4190 J/kg · K and the heat of fusion is 3.34 × 10⁵ J/kg.The specific heat for the metal is closest to

In a thermodynamic process involving 7.8 moles of an ideal gas,the gas is at an initial temperature of 24°C and has an initial volume of 0.040 m³.The gas expands adiabatically to a volume of 0.080 m³.For this gas,C_V = 12.27 J/mol · K,and the ideal gas constant is R = 8.314 J/mol ∙ K.Calculate the work done by the gas during this expansion.

A solid metal sphere is 15.0 cm in diameter and has surface of uniform color.When its surface is at 112°C,you measure that it radiates energy at a rate of 71.3 W.What is the emissivity of the surface of this object? Any heat that enters the sphere from the outside environment is negligible.The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

A copper cylinder with a mass of 125 g and temperature of 345°C is cooled by dropping it into a glass beaker containing 565 g of water initially at 20.0°C.The mass of the beaker is 50.0 g and the specific heat of the glass is 840 J/kg ∙ K.What is the final equilibrium temperature of the system,assuming the cooling takes place very quickly,so that no energy is lost to the air? The specific heat of copper is 385 J/kg ∙ K and that of water is 4190 J/kg ∙ K.

3.0 moles of an ideal gas with a molar heat capacity at constant volume of 4.9 cal/(mol ∙ K)and a molar heat capacity at constant pressure of 6.9 cal/(mol ∙ K)starts at 300 K and is heated at constant pressure to 320 K,then cooled at constant volume to its original temperature.How much heat flows into the gas during this two-step process?

During an isothermal process,5.0 J of heat is removed from an ideal gas.What is the change in internal (thermal)energy of the gas?

When a fixed amount of ideal gas goes through an adiabatic expansion,

If you add 700 kJ of heat to 700 g of water at 70.0°C,how much water is left in the container? The latent heat of vaporization of water is 2.26 × J/kg and its specific heat is 4190 J/(kg ∙ K).

An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed.If its final temperature is 400 K and γ = 1.30,what is its final volume?

Under steady state conditions,a piece of wood 350 mm by 350 mm and 15 mm thick conducts heat through its thickness and loses no appreciable heat through its well-insulated sides.The rate of heat flow is measured to be 14.0 W when the temperature difference across its thickness is 28°C.Determine the thermal conductivity of this wood.

An ideal gas is allowed to expand slowly at constant temperature to twice its original volume.During the expansion,the gas absorbs 200 kJ of heat. (a)What is the change in the internal (thermal)energy of the gas during the expansion? (b)How much work does the gas do during the expansion?

A radiating body originally has a Kelvin temperature T_o,and its surroundings are at 500K (T_o > 500K).If the Kelvin temperature of the radiating body is increased to ,the net rate at which the body radiates increases by a factor of 333.What was the original temperature ?

A monatomic ideal gas undergoes an isothermal expansion at 300 K,as the volume increased from to The final pressure is The ideal gas constant is R = 8.314 J/mol ∙ K.The heat transfer to the gas is closest to

The process shown in the pV diagram in the figure is an

The figure shows a pV diagram for 0.0066 mol of gas that undergoes the process 1 → 2 → 3.What is the pressure p₂? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.