The pressurized cabin of a spacecraft contains a nitrogen-oxygen gas mixture at a temperature of 22.0 ∘C22.0\ ^\circ\text{C}22.0 ∘C and a pressure of 98.0 kPa98.0\text{ kPa}98.0 kPa.
Show that the amount of gas in each cubic metre of the cabin is about 40 mol40\text{ mol}40 mol.
The density of the cabin gas mixture is 1.16 kg m−31.16\text{ kg m}^{-3}1.16 kg m−3. Calculate crmsc_{\text{rms}}crms for the gas molecules. Give your answer to an appropriate number of significant figures.
Calculate, in K\text{K}K, the change of temperature that will triple crmsc_{\text{rms}}crms for the gas molecules.
An environmental control system manages the cabin humidity. Humid air at a temperature of 22 ∘C22\ ^\circ\text{C}22 ∘C enters a condensing unit. The unit cools and condenses water vapour from the humid air. The final temperature of the liquid water that collects in the condensing unit is 6 ∘C6\ ^\circ\text{C}6 ∘C. Drier air leaves the unit at a temperature of 22 ∘C22\ ^\circ\text{C}22 ∘C.
Table 1 compares the cabin air flowing into and out from the condensing unit:
| mass of watermass of air\frac{\text{mass of water}}{\text{mass of air}}mass of airmass of water | |
|---|---|
| humid air flowing in | 0.00850.00850.0085 |
| drier air flowing out | 0.00450.00450.0045 |
In one hour, a volume of 850 m3850\text{ m}^3850 m3 of air flows through the condensing unit. Assume that the density of the air remains constant at 1.16 kg m−31.16\text{ kg m}^{-3}1.16 kg m−3.
Determine how much heat energy is removed in one hour from the water vapour by the condensing unit.
