The following four air parcels A, B, C and D are given with their temperatures (T) and water vapour mixing ratios (w). Arrange the air parcels in asce

Question

The following four air parcels A, B, C and D are given with their temperatures (T) and water vapour mixing ratios (w). Arrange the air parcels in ascending order of their virtual temperatures.
A. $T=30^∘ C and w=5" " g/kg$
B. $T=20^∘ C$ and w=15" " g/kg
C. $T=30^∘ C$ and w=25" " g/kg
D. $T=20^∘ C$ and w=30" " g/kg
Choose the correct answer from the options given below:

A, B, C, D

D, C, B, A

D, B, C, A

B, D, A, C

Solution

Correct option is D

Introduction

Virtual temperature is the temperature that dry air would need to have the same density as a given sample of moist air at the same pressure.

Because water vapour is less dense than dry air, adding moisture always raises the virtual temperature above the actual temperature.

Information Booster

Virtual temperature (T_v) is calculated using the relation:
T_v ≈ T (1 + 0.61 w)
where T is the actual temperature in kelvin and w is the water-vapour mixing ratio (in kg/kg).

The factor 0.61 arises from the ratio of the molecular weights of dry air and water vapour, and it captures how moisture lowers air density an effect represented as an equivalent temperature increase.

The key insight is that virtual temperature depends on both the actual temperature and the moisture content.

A parcel that is cooler but very moist can have a higher virtual temperature than a warmer but drier parcel, because the moisture correction (0.61w) can outweigh a small temperature difference. To rank the parcels, one computes T_v for each by:
1. Converting each temperature to kelvin,
2. Ensuring the mixing ratio w is in kg/kg (not g/kg),
3. Applying T_v = T(1 + 0.61w),
4. Comparing the resulting values in ascending order.
For the given data, this procedure yields the sequence, placing parcel B with the lowest virtual temperature and parcel C with the highest.