Question

(10%) Problem 7: Alarge room contains a volume of air of V.-19m3 at a holding a volume of water of v-0.79 m2 at a temperature of T-103* temperature of T, S2 F. Italso contains a bathcub e for view ▲ 20% Part (a) If the density of the air at Ta is e.-125 kg/m3, calculate the mass of air in the room in kilograms. artial 20% Part (b) If the density of the water at Tw is ew-1000 kg/m, calculate the mass of the water in the bathtub in kilograms, 2O% Part (c) Take the room and water as an isolated system wnte an equation for the equilibrium temperature of the system Tin terms of ma. and the specific heat capacity of the air ca and the water c Tam T Grade Summary Potential: 100% Atempts remaining TE 3% per attempt) ca l give up Hint constant specific heat capacity for the air of ca 1010 J/kg K 20% Part (e) Calculate the change in the internal energy AU of the

Answer 1

7

a)

V_a = Volume of air = 19 m³

$\rho _{a}$ = density of air = 1.25 kg/m³

mass of air is given as

m_a = $\rho _{a}$ V_a

m_a = (1.25) (19)

m_a = 23.75 kg

b)

V_w = Volume of water = 0.79 m³

$\rho _{w}$ = density of water = 1000 kg/m³

mass of air is given as

m_w = $\rho _{w}$ V_w

m_w = (1000) (0.79)

m_w = 790 kg

c)

T = equilibrium temperature

Using conservation of heat

Heat lost by water = Heat gained by air

m_w c_w (T_w - T) = m_a c_a (T - T_a )

m_w c_w T_w + m_a c_a T_a = (m_w c_w + m_a c_a )T

T = (m_w c_w T_w + m_a c_a T_a )/(m_w c_w + m_a c_a )