Question

A certain fluid at 10bar is contained in a cylinder behind a piston, the initial volume being 0.05m^3. Calculate the work done by the fluid when it expands reversibly: 1. According to a linear law to a final volume of 0.2m^3 and a final pressure of 2 bar. 2 according to a law, p=(A/V^2)-(B/V), to a final volume of 0.1m^3 and a final pressure of 1bar, where A and B are constants. Sketch the processes on a P-V diagram.

Answer 1

Answer on Question #45385, Physics, Molecular Physics | Thermodynamics

Task: A certain fluid at 10bar is contained in a cylinder behind a piston, the initial volume being $0.05\mathrm{m}^3$ . Calculate the work done by the fluid when it expands reversibly: 1. According to a linear law to a final volume of $0.2\mathrm{m}^3$ and a final pressure of 2 bar. 2 according to a law, $p = (A / V^2) - (B / V)$ , to a final volume of $0.1\mathrm{m}^3$ and a final pressure of 1bar, where A and B are constants. Sketch the processes on a P-V diagram.

Solution:

$$W = P d v = P (V 2 - V 1) = 1000 \, \text{kPa} * (.2 - .05) = 150 \, \text{kJ}$$ $$W = \text{area under curve} \, s_o = P 2 * d v + .5 * d v * d p = 200 * .15 + .5 * .15 * 800 = 90 \, \text{kJ}$$ $$W = P 1 V 1 * \ln (V 2 / V 1) = 1000 * .05 * \ln (1 / .05) = 34.7 \, \text{kJ}$$ $$W = (p 2 v 2 - p 1 v 1) / 1 - n \, \text{when} \, p 2 = p 1 * (V 1 / V 2) ^ {3} = 1.25 \, \text{bar}$$ $$W = (125 * .1 - 1000 * .05) / -2 = 18.75 \, \text{kJ}$$

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