Absolute humidity in atmosphere at $ 10^\circ $ is $5.0$ g/m$^3$ and maximum amount of water air can hold at same temperature is $ 10$ g m$^3$. What will be the relative humidity at the same temperature?
Relative humidity (RH) indicates the amount of water vapor present in the air compared to the maximum amount the air could hold at a specific temperature. It's expressed as a percentage.
The formula to calculate relative humidity is:
$ \text{Relative Humidity (RH)} = \frac{\text{Absolute Humidity (AH)}}{\text{Saturation Humidity (SH)}} \times 100\% $
Given values:
Substitute these values into the formula:
$ \text{RH} = \frac{5.0 \text{ g/m}^3}{10 \text{ g/m}^3} \times 100\% $
Performing the calculation:
$ \text{RH} = 0.5 \times 100\% $
$ \text{RH} = 50\% $
Therefore, the relative humidity at $10^\circ$ C is $50\%$.