Question

What is the value of mass of the air in a room of size 4m × 5m × 6m at 100 kPa and 25°C ? (Take R = 0.287 kPa.m³.kg^-1).K^-1) 
1. 150 kg
2. 180 kg
3. 140 kg
4. 130 kg
5.

Answer 1

Correct Answer - Option 3 : 140 kg

Concept:

A hypothetical gas that obeys the law ideal-gas law at all pressures and temperatures is called Ideal gas. There are two equations for Ideal Gas.

• PV = nR̅T
• PV = mRT, P = ρRT

Calculation:

Given:

Volume = 4m × 5m × 6m, P₁ = 100 kPa, T₁ = 25°C = 298 K.

R = 0.287 kPa.m3.kg-1.K-1 = 0.287 kJ/kgK.

PV = mRT

100 × (4 × 5 × 6) = m × 0.287 × 300

∴ m = 139.37 kg ≈ 140 kg.