A balloon made of rubber and filled with air has a volume of 1 m³ under standard conditions of pressure and temperature. What is the volume of the balloon (V_Mars) if it is placed outside a Martian station where the pressure and temperature are 600 Pa and -60 °C, respectively? Assume that the balloon will not burst on Mars.

A certain amount of carbon dioxide gas occupies a volume of 50 liters. The gas is at room temperature (25°C) and under normal atmospheric pressure (about one atmosphere). What would be the new pressure if we compressed this gas into a volume of 25 liters and increased the temperature by 15°C so that the new temperature would reach 40°C?

Determine the sum of the translational kinetic energy of air at 1 atm in a metallic tank measuring 10.0 m by 6.0 m by 4.0 m. Assume the tank is full of air that behaves like an ideal gas.

An oxygen cylinder for scuba diving is placed horizontally on the ground. Consider that 5.0 × 10²⁴ oxygen molecules moving at 485 m/s in the x direction collide head-on with a 50 cm² walled section of cylinder each second. Determine the pressure exerted by the oxygen on the walled section.

A rigid insulator container is divided into two compartments by a thin membrane. The left compartment contains n_ar moles of argon gas (monoatomic), while the right compartment contains n_ni moles of nitrogen gas (diatomic). Two temperature sensors, one placed in the left compartment and one in the right compartment, measure T_ar and T_ni respectively. The membrane prevents any mixing of the gases. Find the final temperature T_f of the system in terms of n_ar, n_ni, T_ar, and T_ni when thermal equilibrium is reached.

In a physics simulation, four particles are moving with unique velocities as follows:
v₁ = (10î - 20ĵ) m/s
v₂ = (30î + 40ĵ) m/s
v₃ = (-40î + 10ĵ) m/s
v₄ = (20î - 30ĵ) m/s

Determine i) Average velocity (v_avg), ii) Average speed (v_avg), and iii) Root-mean-square velocity (v_rms) of the particles in the simulation.

In an experiment, a 3.0 g sample of argon gas was enclosed in a special chamber. If the rms speed of the atoms inside the chamber is 900 m/s, determine the total thermal energy of the argon gas.

A hot air balloon uses a mixture of 60% nitrogen and 40% helium. The balloon has a volume of 2500 cm³. What is the ratio of the average kinetic energies of these two types of molecules, nitrogen to helium, respectively?

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?