Using the ideal gas law equation of P=NkT/V, show that: a) a container of gas obeys Boyle's Law, which states that if the temperature of the gas is held constant, the pressure of the gas is proportional to its volume. b) a container of gas obeys Gay-Lussac's which states that, if the volume of a container is held constant, the pressure is proportional to its temperature.  c) if the pressure is held constant, the temperature is related to volume. Draw a sketch showing how V varies as a function of T if P is held constant.

2. Consider a monatomic gas in a 2-dimensional box with a rectangular area A. The velocity distribution for this gas is given by (you do not need to prove this): {-m (C +C)/ 2kT} f (C,,C,)=A e Find: A, the speed distribution, and the mean speed, C.

The viscosity (η) of a gas depends on its mass, effective diameter, and average molecular velocity of the gas. Estimate the effective diameter of the methane molecule (CH4) if the η value for helium is ηHe = 2.0 × 10−5 kg / ms and methane is ηCH4 = 1.1 × 10−5 kg / ms at room temperature, and the effective diameter helium is dHe = 2.1 × 10−10 m! A. 2 x 10-8 m B. 4 x 10-10 m C. 2 x 10-10 m D. 4 x 10-8 m

Case 1: A container with argon gas is sealed by a movable heavy piston with cross [ sectional area, A. Initially, the piston is in equilibrium, the volume of the gas is V1, and the system is in thermal equilibrium. The piston is then slowly lifted by external force to a distance, L, at constant pressure P1. After that, the piston is not allowed to move while the pressure is reduced to P2. Case 2: A container with argon gas is sealed by a movable heavy piston with cross sectional area, A. Initially, the piston is in equilibrium, the pressure of the gas is P1, and the system is in thermal equilibrium. The piston is then not allowed to move while the pressure is reduced to P2. After that, the piston is then slowly lifted by external force to a distance, L, at constant pressure P2. Identify which case require more work by the argon? Justify your answer.

Three moles of an ideal monatomic gas expands at a constant pressure of 2.10 atmatm ; the volume of the gas changes from 3.00×10−2 m3m3 to 4.30×10−2 m3m3 . Part A) Calculate the initial temperature of the gas. Tinital= -------K Part B) Calculate the final temperature of the gas. Tfinal= --------K Part C) Calculate the amount of work the gas does in expanding. W= ------J Part D) Calculate the amount of heat added to the gas. Q= -------J Part E) Calculate the change in internal energy of the gas.

Problem 3: Consider a stationary horizontal slab of air of height dz. Since the slab is at rest, the pressure p holding it up from below must be balanced by the pressure from above PLUS the weight of the slab. a) Derive a formula for dP/dz the variation of pressure with altitude, in terms of the mass density p (greek letter rho) of the air. b) Using the ideal gas law, rewrite the air density in terms of the average mass m of the air molecules and other variables. Combine your result with part (a) to derive a differential equation relating dP/dz to P. Show then that pressure obeys the differential equation: dP тg dz kT c) Assume constant temperature T and solve the differential equation in part (b) for pressure P as a function of height z. Assume that P(z=0) is given. Show that the pressure obeys: P = P(0)e-mgz /kT Show also that the density obeys a similar equation.

A fixed amount of gas occupies a volume of 1.75L and exerts a pressure of 95kpa on the walls of its container . What would be the pressure exerted by the gas if it's completely transferred into a new container having a volume of 0.5L(assuming the temperature and quantity of gas remains constant)

A vessel contains an ideal gas with temperature of -15°C, a density of 0.16 kg/m3, and a molecular weight of 4 g/mol. A) What is the pressure of this gas in kPa? B) Its gage pressure? C) If the vessel were punctured which way would gas flow - gas exiting the hole or atmosphere entering the hole? (Ri = 8.314 kg-m2/K-mol-s?)

A hot air balloon uses the principle of buoyancy to create lift. By making the air inside the balloon less dense then the surrounding air, the balloon is able to lift objects many times its own weight. A large hot air balloon has a maximum balloon volume of 2090 m3   a. What is the density of air inside the balloon, in terms of the pressure P, temperature T, molar mass M, and the gas constant R?  b. How much mass can this balloon lift (in addition to the mass of the gas inside) in terms the balloon volume Vb, the atmosphere air density ρa, the density of the air in the balloon ρg, and the gravitational acceleration g?  c.  If the air temperature in the balloon is 54 °C, how much additional mass, in kilograms, can the balloon lift? Assume the molar mass of air is 28.97 g/mol, the air density is 1.20 kg/m3, and the air pressure is 1 atm.

A container of variable volume contains oxygen gas at a pressure of 5.45 atm. What is the new pressure inside the container if the container is allowed to expand from an initial volume of 5.20 L to a final volume to 7.25 L? A) 137 atm B) 7.59 atm OC) 1.13 atm D) 3.91 atm