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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) 

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)  Correct Answer 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.

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