Internal Energy of Gases Practice Problems

What is the specific heat of oxygen (O₂; M = 32.00 g/mol) at constant volume? How does it compare with specific heat for liquid water? Hint: C_v = 20.85 J/mol•K.

2.50 mol of an ideal monoatomic gas is placed in a constant volume container. How much heat should be supplied to raise the temperature of the gas by 44 K at temperatures close to room temperature?

Calculate the heat absorbed by 1.4 moles of an ideal diatomic gas to increase its temperature by 38 K if it is placed in a constant volume container. Assume the process occurs at temperatures near room temperature.

Suppose a region of space has interstellar monoatomic gas (helium atoms only; fictitious though) at a density of 1 atom in every 1000 mm³ and T = 2K. Find the radius, R of a spherical volume of the gas that has 5.0 J of heat energy. 

A 0.32 mol gas sample has its thermal energy as a function of temperature plotted as shown below. Find the heat capacity of the gas at constant volume.

3.2 moles of helium gas with an initial thermal energy of 1750 J is brought to contact (through a conducting boundary) with 2.2 moles of Argon with an initial thermal energy of 12100 J. State the gas with a greater initial temperature.

A mysterious diatomic gas has a strong covalent bond that requires high temperatures to experience vibrational modes. The vibration modes are experienced at temperatures greater than or equal to 1000 K. Suppose the gas enters a combustion chamber of an Otto cycle engine that reaches ignition temperatures of 2400 K; find the theoretical ratio of specific heats of the mysterious gas at 2400 K.

A refrigerator takes out 2.5 J of heat energy from a 4.0 mol of an element. Calculate the decrease in temperature of the element if it is i) Neon, ii) Oxygen, iii) A solid element

A sample of monoatomic gas Y has a volume of 800 mm³, P = 3.0 atm, and T = 150℃. A different sample contains neon at V = 1750 mm³, P = 5.0 atm, and T = 250℃. The two samples are allowed to interact thermally through a boundary. Calculate the thermal energy of each sample when thermal equilibrium is attained. 

A container is filled with 2.4 × 10¹⁹ molecules of a gaseous substance. The heat energy of the gas in the container is 0.80 J. If C_p of the gas is 29.1 J/mol•K, determine the temperature of the gas.

3.2 g of neon at T = 20℃ comes into contact (through a conducting boundary) with 4.2 g of nitrogen at  T =  320℃. Calculate the amount of heat that flows between the gases to establish thermal equilibrium and state the direction of flow.

A hypothetical gas with 4 atoms bonded in a T-shape has a high bond energy that requires temperatures greater or equal to 1200K to activate vibrational modes. The hypothetical gas has rotational kinetic energy in a 3D coordinate system at all temperatures. Calculate the thermal energy of a sample of the gas with n = 6.2 mol, at T = 350 °C. 

2.50 g of nitrogen moves at an rms speed of 1150 m/s. The gas expands, doing 925 J of work to the surroundings, and absorbs 650. J of heat from the surrounding. Calculate the rms speed of the nitrogen molecules after this process.

Consider nitrogen gas (N₂), which behaves similarly to an ideal gas under certain conditions. The molecules of nitrogen have $m$ degrees of freedom, considering both translational and rotational motion. Determine the expressions for the molar heat capacity at constant volume 𝐶_𝑉 and at constant pressure 𝐶_𝑃 for nitrogen gas, using the universal gas constant 𝑅.