Exam 18: The First Law of Thermodynamics

The figure shows a pV diagram for 4.3 g of oxygen gas (O₂) in a sealed container. The temperature T₁ of the gas in state 1 is 21°C. What are the temperatures T₃ and T₄ of the gas in states 3 and 4? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the ATOMIC weight of oxygen is 16 g/mol.

A cylinder contains 24.0 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.63 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K and the ideal gas constant is R = 8.314 J/mol ∙ K. The change in the internal (thermal) energy of the gas is closest to

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

A quantity of ideal gas requires 800 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant volume. The same quantity of gas requires 900 kJ to raise the temperature of the gas by 10.0 K when the gas is maintained at constant pressure. What is the adiabatic constant γ for this gas?

An adiabatic compression is performed on an ideal gas. The final pressure is equal to 0.560 times the initial pressure and the final volume equals 1.50 times the initial volume. What is the adiabatic constant for the gas?

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.

During an adiabatic process, 20 moles of a monatomic ideal gas undergo a temperature change from 450 K to 320 K starting from an initial pressure is 400 kPa. The ideal gas constant is R = 8.314 J/mol ∙ K. (a) What is the final volume of the gas? (b) How much heat does the gas exchange during this process? (c) What is the change in the internal (thermal) energy of the gas during this process?

A cylinder contains 23 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K and the ideal gas constant is R = 8.314 J/mol ∙ K. The heat absorbed by the gas 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 container with rigid walls is filled with 4 mol of air with CV = 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.

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 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.

The figure (not to scale) shows a pV diagram for 1.8 g of helium gas (He) that undergoes the process 1 → 2 → 3. Find the value of V₃. The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the atomic weight of helium is 4.0 g/mol.

The figure shows the pV diagram for a certain thermodynamic process. In this process, 1500 J of heat flows into a system, and at the same time the system expands against a constant external pressure of 9.00 × 10⁴ Pa. If the volume of the system increases from 0.020 m³ to 0.050 m³, calculate the change in internal (thermal) energy of the system. If the internal (thermal) energy change is nonzero, be sure to indicate whether this energy change is positive or negative.

When an ideal gas increases in volume at constant pressure, the average kinetic energy of the gas molecules

A system has a heat source supplying heat to an ideal gas at a rate of 187.0 W and the gas is doing work at a rate of 130.9 W. At what rate is the internal (thermal) energy of the gas changing?

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?

An ideal gas is compressed in a well-insulated chamber using a well-insulated piston. This process is

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, CV = 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 fixed amount of ideal gas goes through a process abc. In state a, the temperature of the gas is 152°C, its pressure is 1.25 atm, and it occupies a volume of 0.250 m³. It then undergoes an isothermal expansion to state b that doubles its volume, followed by an isobaric compression back to its original volume at state c. (Hint: First show this process on a pV diagram.) The ideal gas constant is 8.314 J/mol ∙ K, and 1.00 atm = 1.01 × 10⁵ Pa. (a) How many moles does this gas contain? (b) What is the change in the internal energy of the gas between states a and b? (c) What is the net work done on (or by) this gas during the entire process? (d) What is the temperature of the gas in state c?