Question

A large nitrogen gas bubble is assumed to expand reversibly and adiabatically as it rises through a liquid at 20°C and eventually breaks on the surface. Initially the volume of the bubble is 2 litres and the pressure of the gas in the bubble is 250 kPa. The final pressure of the gas in the bubble just before it reaches the surface is 100 kPa. Using the additional information below, calculate the following:

 

i)     The number of moles of gas in the bubble.

[4 marks]

 

ii)    The final volume of the bubble (just before it reaches the liquid surface).

[4 marks]

 

iii)  The final temperature of the bubble.

[4 marks]

 

iv)  The work done by the expanding bubble.

4 marks

Gas constant 𝑅 = 8.314 JK-1mol-1

Constant pressure molar heat capacity of nitrogen:𝐶𝑝,𝑚 = 29.125 JK-1mol-1

Answer 1

1) $\nu=\frac{p_1V_1}{RT_1}=0.205 ~mol.$

2) $V_2=V_1(\frac{p_1}{p_2})^{\frac 57}=3.85 ~l.$

3) $T_2=T_1(\frac{V_1}{V_2})^{\frac {7}{5}-1}=225~K.$

4) $\Delta U=\frac 52 \nu R\Delta T=-290 ~J.$