1. A) What is the total translational kinetic energy of the air in an empty room

Question

1.

A) What is the total translational kinetic energy of the air in an empty room that has dimensions 7.00 m × 14.00 m × 4.00 m if the air is treated as an ideal gas at 1.00 atm?

B) What is the speed of a 2000-kg automobile if its kinetic energy equals the translational kinetic energy calculated in part A?

2.

A sealed box contains a monatomic ideal gas. The number of gas atoms per unit volume is7.24×1020 atoms/cm3, and the average translational kinetic energy of each atom is 1.20×1023 J .

A) What is the gas pressure?

B)If the gas is neon (molar mass 20.18 g/mol ), what is vrms for the gas atoms?

3.

Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 3.00 atm , then the root-mean-square speed of the helium atoms isvrms = 196 m/s .

A)By how much (in atmospheres) must the pressure be increased to increase the vrms of the He atoms by100 m/s? Ignore any change in the volume of the cylinder.

Explanation / Answer

Ans 1-(A)- translational kinetic energy= 3/2KT

and gas is ideal therefore PV=KT here P and V is known so calculate KT and put in the above question

P= 1.00 atm = 101325 N/m^2 and V= 7x14x4= 686 m^3

KT=101325x686= 6.9 x 10^7 N-m

putting in above equation

Kinetic energy = 3/2 X 6.9 x 10^7 = 10.35 x 10^7 J

Ans 1 - (B)- K.E of automobile= 1/2 mv^2 = translational kinetic energy of gas

therefore 1/2mv^2= 10.35 x 10^7 , ...... m=2000kg(given)

v= 3.2 m/s

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