A cylinder contains 1.2 moles of ideal gas, initially at a temperature of 116?C.

Question

A cylinder contains 1.2 moles of ideal gas, initially at a temperature of 116?C. The cylinder is
provided with a frictionless piston, which maintains a constant pressure of 6.4 × 105 Pa on the
gas. The gas is cooled until its temperature has decreased to 27?C, using CV = 11.65 J/mol.K
find the work done by (or on) the gas during this process. Is the work done by or on the gas?

(1) 1200 J (the positive sign means that work is done on the gas)
(2) -1200 J (the negative sign means that work is done by the gas)
(3) -890 J (the negative sign means that work is done on the gas)
(4) 810 J (the positive sign means that work is done by the gas)
(5) None of the above

Explanation / Answer

Let's get the initial volume first.
PV = nRT
Vi = nRT/P
Vi = 1.2mol * 8.314 m^3·Pa·K^-1·mol^-1 * 389.15 K / 6.4 *10^5 Pa
Vi = 0.00607 m^3
Final volume, by same calculation
Vf = 0.00565 m^3

Work = P * change in V
W = 6.4*10^5 Pa * (0.00565 - 0.00607)m^3
W = -268.8 J

(5) None of the above

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