If the ratio of principal specific heat capacities of a certain gas is 1:4 and its density at STP is 0.09 `kgm^(-3)` calculate the values of specific heat capacity at constant pressure and constant volume. [Standard atmospheric pressure `=1.01 xx 10 ^(5) Nm ^(-2)`

Explanation

To solve the problem, we need to find the specific heat capacities at constant pressure (\(C_p\)) and constant volume (\(C_v\)) for the gas, given the ratio of the specific heat capacities (\(\gamma\)) and the density at standard temperature and pressure (STP).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Ratio of specific heat capacities: \(\gamma = \frac{C_p}{C_v} = \frac{1}{4}\)
- Density at STP: \(\rho = 0.09 \, \text{kg/m}^3\)
- Standard atmospheric pressure: \(P = 1.01 \times 10^5 \, \text{N/m}^2\)
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