A 0.183 kg sample of gas in a piston-cylinder assembly is compressed from a stat

Question

A 0.183 kg sample of gas in a piston-cylinder assembly is compressed from a state where P(1) = 340 kPa, V(1) = 0.0283 m3 to a state where P(2) = 820 kPa in a polytropic process with n = 1.2. During the process, 2.2 kJ of heat is transferred from the gas to the surroundings. Determine the change in specific internal energy of the gas, ?u, in kJ/kg.
the teacher's answer is 29.78, but I keep getting -29.5255
PV^n = c =340(.0283^1.2) = 4.71653
4.71653 = 820(x^1.2) => x = .013588577 = V(2)
q-w= ?u
w(b) = (P(2)*V(2)-P(1)*V(1))/(1-n) = (820*.013588577-340*.0283)/(1-1.2) = -7.60317 kj
q = 2.2 kj
(q+w(b))/.183kg = -29.5255kJ/kg

Explanation / Answer

Your answer for w(b) is right.
w(b) = (P(2)*V(2)-P(1)*V(1))/(1-n) = (820*.013588577-340*.0283)/(1-1.2) = -7.60317 kj

but now q = -2.2 kj
u = [q - w(b)]/.183 kg = +29.5255 kJ/kg

slight different from your teacher's answer, maybe due to rounded error made by your teacher.

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