Question

2.4 mol of monatomic gas A initially has 4700 J of thermal energy. It interacts with 2.8 mol of monatomic gas B, which initially has 8500 J of thermal energy.

Part A

Which gas has the higher initial temperature?

Gas A.

Gas B.

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Part B

What is the final thermal energy of the gas A?

Express your answer to two significant figures and include the appropriate units.

Ef =

Part C

What is the final thermal energy of the gas B?

Express your answer to two significant figures and include the appropriate units.

Ef =

Answer 1

a)
let TA and Tb are temperatures of the gases A and B

use, UA = (3/2)nA*R*TA

==> TA = 2*UA/(3*nA*R)

= 2*4700/(3*2.4*8.314)

= 157 K

UB = (3/2)nB*R*TB

==> TB = 2*UB/(3*nB*R)

= 2*8500/(3*2.8*8.314)

= 243.4 K

clearly TB > TA

so, gas B is at high temperature.

B) let T is the final temperature

Heat lost by gas B = heat ganined by gas A

(3/2)*nB*R*(TB - T) = (3/2)*nA*R*(T - TA)

nB*(TB - T) = nA*(T - TA)

2.8*(243.3 - T) = 2.4*(T - 157)

T = 203.4 K

so, Final thermal energy of gas A, UAf = (3/2)*nA*R*T

= (3/2)*2.4*8.314*203.4

= 6.1*10^3 J <<<<<<<<<<<----------------Answer

C)

Final thermal energy of gas B, UBf = (3/2)*nB*R*T

= (3/2)*2.8*8.314*203.4

= 7.1*10^3 J <<<<<<<<<<<----------------Answer