Question

A mass of gas at an initial pressure of 28 bar and with an internal energy of 1500 kJ, is contained in a well-insulated cylinder of volume 0.06 m3. The gas is allowed to expand behind a piston until its internal energy is 1400 kJ; the law of expansion is PV2=Constant. Calculate
1. Work done;
2. The final volume;
3. The final pressure;
4. Draw P-V diagram.

Answer 1

Answer on Question #71020, Physics / Molecular Physics | Thermodynamics

A mass of gas at an initial pressure of 28 bar and with an internal energy of $1500\mathrm{kJ}$ , is contained in a well-insulated cylinder of volume $0.06\mathrm{m}^3$ . The gas is allowed to expand behind a piston until its internal energy is $1400\mathrm{kJ}$ ; the law of expansion is $\mathsf{PV}^2 = \mathsf{Constant}$ . Calculate

1. Work done;

2. The final volume;

3. The final pressure;

4. Draw P-V diagram.

Solution:

1) As there is no heat transfer in the system: $A = \Delta U = 140 - 1500 = -100kJ$

2) $A = \int p dV = [pV^2 = C] = -C\int \frac{1}{V^2} dV = C\left(\frac{1}{V_2} -\frac{1}{V_1}\right) = p_1V_1^2\left(\frac{1}{V_2} -\frac{1}{V_1}\right) = -100kJ$

As we know, $V_{1} = 0.06 \, m^{3}, p_{1} = 28 \, \text{bar},$ then $V_{2} = 0.148 \, m^{3}$

3) $p_2 = \frac{p_1V_1^2}{V_2^2} = 28*\frac{0.06^2}{0.148^2} = 4.6$ bar

4)

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