First slide

Thermodynamic processes

Question

An ideal gas is taken through quasi static process described by $P = α V^{2},$ with $α = 5.00 a t m / m^{6}$ . The gas is expanded to twice its original volume of $1 m^{3}$ how much
work is done by the gas in expanding gas in this process?

Moderate

A

$1.18 M J$
B

$2.18 M J$
C

$1.28 M J$
D

$3.18 M J$

Solution

$\begin{array}{l} W = \int_{i}^{f} p d v \\ W = \int_{i}^{f} α V^{2} d V = \frac{1}{3} α (V_{f}^{3} - V_{1}^{3}) ∣ \\ V_{f} = 2 V_{i} = 2 (1.00) = 2.00 m^{3} \\ W = \frac{1}{3} [5 \times 1.013 \times 10^{5}] \times [2^{3} - 1^{3}] = 1.18 M J \end{array}$

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