Question

The density of helium gas at 0.0 ◦C is 0.16 kg/m3 kg/m3. The temperature is then raised to 100.6 ◦C, but the pressure is kept constant. Assuming that helium is an ideal gas, calculate the new density of the gas. Answer in units of kg/m3.

Answer 1

Answer:

0.11694 kg/m³

Explanation:

T₁ = 0.0 °C = 273.15 K

ρ₁ = Density = 0.16 kg/m³

T₂ = 100.6 °C = 373.72 °C

PV = mRT

Realtion with density

$Pm=\rho RT\\\Rightarrow \rho =\frac{Pm}{RT}\\\Rightarrow \rho T= \frac{Pm}{R}$

P, m and R are constants, so

$\rho_1 T_1=\rho_2 T_2\\\Rightarrow \rho_2=\frac{\rho_1 T_1}{T_2}\\\Rightarrow \rho_2=\frac{0.16\times 273.15}{373.72}\\\Rightarrow \rho_2=0.11694\ kg/m^3$

∴ New density of the gas is 0.11694 kg/m³