An ideal gas is taken through a quasi-static process described by P=α V2, with α=5.00 atm / m 6 . The gas is expanded to twice its original volume of 1.00 m 3. How much work is done by the gas in expanding gas in this process?

Question

An ideal gas is taken through a quasi-static process described by P=α V2, with α=5.00 atm / m 6 . The gas is expanded to twice its original volume of 1.00 m 3. How much work is done by the gas in expanding gas in this process? (A) 1.18 MJ (B) 2.18 MJ (C) 1.28 MJ (D) 3.18 MJ

Tardigrade Admin · Accepted Answer

The work done by the gas W =∫ limitsif P d V W =∫ limitsif α V2 d V=(1/3) α(Vf3-Vi3) Vf =2 Vi=2(1.00 m 3)=2.00 m 3 W =(1/3) [(5.00 atm / m 6)(1.013 × 105 Pa / atm )] ×[(2.00 m 3)3-(1.00 m 3)3]=1.18 MJ

Q. An ideal gas is taken through a 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 $1.00 m^{3}$ . How much work is done by the gas in expanding gas in this process?

1.18 MJ

2.18 MJ

1.28 MJ

3.18 MJ

The work done by the gas
$W = i \int f P d V$
$W = i \int f α V^{2} d V = \frac{1}{3} α (V_{f}^{3} - V_{i}^{3})$
$V_{f} = 2 V_{i} = 2 (1.00 m^{3}) = 2.00 m^{3}$
$W = \frac{1}{3} [(5.00 a t m / m^{6}) (1.013 \times 1 0^{5} P a / a t m)]$
$\times [(2.00 m^{3})^{3} - (1.00 m^{3})^{3}] = 1.18 M J$

Q. An ideal gas is taken through a quasi-static process described by P=αV2, with α=5.00atm/m6. The gas is expanded to twice its original volume of 1.00m3. How much work is done by the gas in expanding gas in this process?