2.5 g of helium at an initial temperature of 300 K interacts thermally with 9.0 g of oxygen at an initial temperature of 620 K. A) What is the initial thermal energy of each gas?

B) What is the final thermal energy of each gas?

C) How much heat energy is transferred, and in which direction?

D) From He to O2 or O2 to He

E) What is the final temperature?

2.5 g of He = 2.5 / 4 mole

=.625 moles

9 g of oxygen = 9/32

=.28 mole of oxygen

C_p of He = 3/2 R

C_p of O₂ = 5/2 R

A) Initial thermal energy of He = 3/2 n R T

= 1.5 x. 625 x 8.32 x 300

= 2340 J

Initial thermal energy of O₂ = 5/2 n R T

= 2.5 x. 28 x 8.32 x 620

= 3610.88 J

B) If T be the equilibrium temperature after mixing

gain of heat by helium

= n C_p Δ T

=.625 x 3/2 R x (T - 300)

Loss of heat by oxygen

n C_p Δ T

=.28 x 5/2 R x (620 - T)

Loss of heat = gain of heat

.625 x 3/2 R x (T - 300) =.28 x 5/2 R x (620 - T)

1.875 T - 562.5 = 868 - 1.4 T

3.275 T = 1430,5

T = 436.8 K

Thermal energy of He

= 1.5 x. 625 x 8.32 x 436.8

= 3407 J

thermal energy of O₂

= 2.5 x. 28 x 8.32 x 436.8

= 2543.92 J

C)

Heat energy transferred

=.28 x 5/2 R x (620 - T)

=.28 x 5/2 x 8.32 x (620 - 436.8)

1066.95 J

Heat will flow from O₂ to He

Final temperature is 436.8 K