Question

A unit mass of carbon dioxide gas is contained in a cylinder behind a piston and is heated from p1 = 552 kPa and V1 = 0.0184 m3
to p2 = 138 kPa. It expands acc
ording to a law pV1.3 = constant and the heat supplied to the gas during
the expansion process is 10.125 kJ. Calculate, per unit of mass:
(a) the work done during the of expansion process.
(b) the change in the internal energy of carbon dioxide.

Answer 1

a)

$$W=\int^{V_2}_{V_1}pdV$$

$$pV^{1.3}=C$$

$$p_1V_1^{1.3}=p_2V_2^{1.3}\to (552)0.0184^{1.3}=(138)V_2^{1.3}$$

$$V_2=0.0534\ m^3$$

$$W=p_1V_1^{1.3}\int^{V_2}_{V_1}V^{-1.3}dV$$

$$W=\frac{1}{0.3}p_1V_1^{1.3}(V^{-0.3}_1-V^{-0.3}_2)$$

$$W=\frac{1}{0.3}(552000)0.0184^{1.3}(0.0184^{-0.3}_1-0.0534^{-0.3}_2)$$

$$W=9269\ J=9.269\ kJ$$

b)

$$\Delta U=Q-W=10125-9269=856\ J$$