Exam 17: Work, Heat, and the First Law of Thermodynamics

A container with rigid walls is filled with 4 mol of air with C_V = 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

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

An ideal gas with γ = 1.67 is initially at 0°C in a volume of 10.0 L at a pressure of 1.00 atm. It is then expanded adiabatically to a volume of 10.4 L. What is the final temperature of the gas?

A spherical object 25.0 cm in diameter having an emissivity of 0.800 is held at a temperature of 275°C by an internal heater. This object is embedded in a very large vat of water at 100.0°C and atmospheric pressure. At what maximum rate (in g/min) is the water evaporating in the vat due to the radiated heat it receives from the object? You can ignore any heat radiated by the water. The latent heat of fusion for water is 33,400 J/kg, its latent heat of vaporization is 2.26 × 10⁶ J/kg, and the Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴.

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much work does the gas do during this 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?

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?

The figure shows a pV diagram for 8.3 g of nitrogen gas (N₂) in a sealed container. The temperature T₁ of the gas in state 1 is 79°C. What are (a) the pressure p₁ of the gas in state 1 and (b) the temperature T₂ of the gas in state 2? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the ATOMIC weight of nitrogen is 14 g/mol.

A certain amount of ideal monatomic gas is maintained at constant volume as it is cooled from 455K to 405 K. This feat is accomplished by removing 400 J of heat from the gas. How much work is done by the gas during this process? The ideal gas constant is R = 8.314 J/mol ∙ K.

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.

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

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?

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.

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.

When a fixed amount of ideal gas goes through an isochoric process

When a fixed amount of ideal gas goes through an isothermal expansion

An ideal gas increases in temperature from 22°C to 42°C by two different processes. In one process, the temperature increases at constant volume, and in the other process the temperature increases at constant pressure. Which of the following statements about this gas are correct? (There may be more than one correct choice.)

The temperature of an ideal gas in a sealed 0.40 m³ container is reduced from 400 K to 270 K. The final pressure of the gas is 30 kPA. The molar heat capacity at constant volume of the gas is 28.0 J/mol · K. The work done by the gas is closest to

When a vapor condenses

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.