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A large room contains a volume of air of Va = 18 m3 at a temperature of Ta = 59° F. It also contains a bathtub holding a volume of water of Vw = 0.81 m3 at a temperature of Tw = 116° F.a. If the density of the air at Ta is ga = 1.25 kg/m3, calculate the mass of air in the room in kilograms.b. If the density of the water at Tw is gw = 1000 kg/m3, calculate the mass of the water in the bathtub in kilograms.

Respuesta :

Answer:

[tex]m_a=22.5\ kg[/tex] is the mass of air.

[tex]m_w=810\ kg[/tex] is the mass of water.

Explanation:

Given:

  • Volume of air, [tex]V_a=18\ m^3[/tex]
  • temperature of air, [tex]T_a=59^{\circ}C[/tex]
  • volume of water in tub, [tex]V_w=0.81\ m^3[/tex]
  • temperature of water in the tub, [tex]T_w=116^{\circ}C[/tex]
  • density of air, [tex]\rho_a=1.25\ kg.m^{-3}[/tex]
  • density of water, [tex]\rho_w=1000\ kg.m^{-3}[/tex]

We know:

[tex]\rm density=\frac{mass}{volume}[/tex]

So, mass of air in the room :

[tex]\rho_a=\frac{m_a}{V_a}[/tex]

[tex]1.25=\frac{m_a}{18}[/tex]

[tex]m_a=22.5\ kg[/tex]

Mass of water in the tub:

[tex]\rho_w=\frac{m_w}{V_w}[/tex]

[tex]1000=\frac{m_w}{0.81}[/tex]

[tex]m_w=810\ kg[/tex]

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