Consider a reversible adiabatic expansion of 1.00 mol of an ideal gas, starting

Question

Consider a reversible adiabatic expansion of 1.00 mol of an ideal gas, starting from 1.70 L and 435 K, if 1.6 kJ of work is done by the expansion. The molar heat capacity at constant volume of the gas is 2.5R R= 8.314 JK^-1 mol^-1 Determine the final temperature of the gas in the process. Express your answer to three significant figures and include the appropriate units. Determine the final volume of the gas in the process. Express your answer to two significant figures and include the appropriate units. Determine the final pressure of the gas in the process.

Explanation / Answer

Part A.

Using the equation,

w = Cv(T2-T1)

where,

Cv = 2.5 R (R = 8.314 J/K.mol)

T1 = 435 K

T2 = unknown

w = 1.6 kJ

Feed values,

1600 = 2.5 x 8.314 (T2-435)

T2 = 511.98 K is the final temperature of the gas

Part 2.

We will use the expression,

(T2/T1) = (V2/V1)^(5/3-1)

Feed all the values,

511.98/435 = (V2/1.7)^0.667

1.177 = (V2/1.7)^0.667

taking log on both sides,

log(1.177) = 0.667log(V2/1.7)

V2 = 2.2 L is the final volume of the gas

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