Compute the specific heat at constant volume of nitrogen (N₂) gas, and compare it with the specific heat of liquid water. The molar mass of N₂ is $28.0$ g/mol.

Smoke particles in the air typically have masses of the order of ${10}^{-16}$ kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. Find the root-mean-square speed of Brownian motion for a particle with a mass of $3.00\times {10}^{-16}$ kg in air at $300$ K.

How much heat does it take to increase the temperature of $1.80$ mol of an ideal gas by $50.0$ K near room temperature if the gas is held at constant volume and is diatomic?

How much heat does it take to increase the temperature of $1.80$ mol of an ideal gas by $50.0$ K near room temperature if the gas is held at constant volume and is monatomic?

For diatomic carbon dioxide gas (CO₂, molar mass $44.0$ g/mol) at $T = 300$ K, calculate the most probable speed $v_{mp}$.

For diatomic carbon dioxide gas (CO₂, molar mass $44.0$ g/mol) at $T = 300$ K, calculate the average speed $v_{av}$.

For diatomic carbon dioxide gas (CO₂, molar mass $44.0$ g/mol) at $T=300$ K, calculate the root-mean-square speed $v_{rms}$.