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Physics Question on Thermodynamics

A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27∘ C27^\circ\,C. Its density is :(R=8.3 J mol−1K−1(R = 8.3\,J\,mol^{-1}K^{-1})

A

0.5 kg/m30.5 \,kg/m^3

B

0.2 kg/m30.2 \,kg/m^3

C

0.1 kg/m30.1 \,kg/m^3

D

0.02 kg/m30.02 \,kg/m^3

Answer

0.2 kg/m30.2 \,kg/m^3

Explanation

Solution

We can express, an ideal gas equation as
Pρ=R.TMw\frac{P}{\rho}=\frac{R.T}{Mw}
⇒ρ=pMwRT\Rightarrow \rho=\frac{pMw}{RT}
=249×103×2×10−38.314×300=\frac{249 \times 10^{3}\times 2 \times 10^{-3}}{8.314 \times 300}
=0.199=0.199
⇒ρ=0.2kg/m3\Rightarrow \rho=0.2 kg/m^{3}