Question

Air in a thundercloud expands as it rises. If its initial temperature is 300 K and no energy is lost by thermal con- duction on expansion, what is its temperature when the ini- tial volume has doubled

Answer 1

Answer:

$T_{f}=227K$

Explanation:

Given data

Initial temperature of air Ti=300 K

Vf (final volume of air)=2Vi (initial volume of air )

To find

Final temperature

Solution

Since no energy is lost by thermal conduction during the process we categorize  this process as an adiabatic one.Hence we apply;

$T_{i}V_{i}^{Y-1}=T_{f}V_{f}^{Y-1}\\T_{f}=T_{i}(\frac{V_{i}}{V_{f}} )^{Y-1}$

Where air is predominantly a diatomic gas Y=1.4m

Substitute the given values

So

$T_{f}=300K(\frac{V_{i}}{2V_{i}} )^{1.4-1}\\T_{f}=227K$