(i) State the assumptions made in deriving the expression P = pc² for a fixed mass of deal gas. (ii) Estimate the Kinetic energy of a steam molecule at 11 00C.

3) In a cylinder 6 moles of natural gas (M-19.09 x 10* kg/mole) is at 40°C temperature. Calculate for the gas: (R-8.31 J/kg-mole K and KB -1.38 x 10-3 J/K) (a) the average kinetic energy of a molecule, (b) the total random kinetic energy of all the molecules, and (c) the rms speed of a molecule

i) In a cylinder 4 moles of Helium gas (M= 4.02 x 103 kg/mole) is at 30 °C temperature. Calculate for the gas: (R=8.31 J/kg-mole K and KB =1.38 x 10-3 J/K) (a) the average kinetic energy of a molecule, (b) the total random kinetic energy of all the molecules, and (c) the rms speed of a molecule

(a) An ideal gas occupies a volume of 2.6 cm at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container. molecules (b) If the pressure of the 2.6-cm volume is reduced to 1.8 x 10-11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container? mol

(1) Calculate the rms (root-mean-square) speed of hydrogen (H2), helium (He), and oxygen (O2) at room temperature. These speeds are very high. Evaluate these speeds against the escape velocity from the Earth, ~11.2 [km/s].

(a) An ideal gas occupies a volume of 1.2 cm³ at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container. molecules (b) If the pressure of the 1.2-cm³ volume is reduced to 2.2 x 10-11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container? mol

iii) An ideal gas with an initial pressure of 4 x10 Pa and an initial volume of 3 m expands isothermally (at constant temperature) to a volume of 8 m Estimate the final pressure of the gas.

(a) How many atoms of helium gas fill a spherical balloon of diameter 30.2 cm at 17.0°C and 1.00 atm?atoms(b) What is the average kinetic energy of the helium atoms?J(c) What is the rms speed of the helium atoms?km/s

a) At what temperature do oxygen molecules have the same average speed as helium atoms (M = 4.00 g/mol) have at 300 K? b) What is the answer to the same question about most probable speeds? c) What is the answer to thesame question about rms speeds?