Part A An ideal gaseous reaction (which is a hypothetical gaseous reaction that

Question

Part A An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing gas behavior) occurs at a constant pressure of 30.0 atm and releases 72.1 kJ of heat. Before the reaction, the volume of the system was 7.60 L . After the reaction, the volume of the system was 2.80 L . Calculate the total internal energy change, U, in kilojoules.

Part B An ideal gas (which is is a hypothetical gas that conforms to the laws governing gas behavior) confined to a container with a massless piston at the top. (Figure 2) A massless wire is attached to the piston. When an external pressure of 2.00 atm is applied to the wire, the gas compresses from 4.90 to 2.45 L . When the external pressure is increased to 2.50 atm, the gas further compresses from 2.45 to 1.96 L . In a separate experiment with the same initial conditions, a pressure of 2.50 atm was applied to the ideal gas, decreasing its volume from 4.90 to 1.96 L in one step. If the final temperature was the same for both processes, what is the difference between q for the two-step process and q for the one-step process in joules?

Explanation / Answer

A) we know that

at constant pressure

work = P ( V2 - V1)

also

1 atm = 101325 Pa

1 L = 10-3 m3

so

using given values

work (W) = 30 x 101325 x ( 2.80 - 7.60 ) x 10-3

work = -14590 J

work = -14.59 kJ

now

we know that

dQ = dU + W

given

dQ = -72.1 kJ

so

-72.1 = dU - 14.59

dU = -57.51 kJ

so

the change in internal energy is -57.51 kJ

B)

we know that

internal energy is a state function

so

the change in internal enrgy is same in both processes

now

work is a path function

so

first process :

Work = PdV

so

work = 2 x ( 2.45 - 4.90) + 2.5 ( 1.96 - 2.45)

work = -4.9 - 1.225

work = -6.125 atm L

so

work = -6.125 x 101325 x 10-3 J

work = -620.6 J

second step :

work = 2.5 x ( 1.96 - 4.90)

work = -7.35 atm L

work = -7.35 x 101325 x 10-3

work   = -744.74 J

so

the difference is

q1 - q2 = ( -620.6 ) - ( -744.74)

q1 - q2 = 124.14

so

the difference is 124.14 J

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