Question

A 400 g block of ice at 0 C is placed inside an empty copper bowl at 30 C". Given enough time, this system reaches a steady state temperature of 5 C". If the system is thermally insulated from the surroundings, what is the mass of the copper bowl? The specific heat capacities of water and copper are 4180 J kg K and 386 J kg'K', respectively. The latent heats of fusion and vaporization of water are 333 kJ kg and 2256 kJ kg', respectively.

A). 15,6 kg
B). 10.2 kg
C). 17.8 kg
D). 14.7 kg

Answer 1

Answer:

D.14.7 kg

Explanation:

Mass of block of ice=$m_i=400 g=400\times 10^{-3} kg$

1 kg=1000 g

$T_1=0^{\circ}C$

$T_2=30^{\circ}C$

$T_3=5^{\circ}C$

Specific heat capacities of water=$C_w=4180J/kgK$

Specific heat capacities of copper=$C=386 J/kgk$

Latent heat of fusion=$L_f=333KJ kg=333\times 10^3 Jkg$

$1KJ=1000 J$

Latent heat of vaporization=$L_v=2256KJkg=2256\times 10^3Jkg$

$m_Cu C(T_2-T_3)=m_iL_f+m_iC_w(T_3-T_1)$

Substitute the values

$m_Cu\times 386(30-5)=400\times 10^{-3}\times 333\times 10^3+400\times 10^{-3}\times 4180(5-0)$

$m_{Cu}(25)(386)=141560$

$m_{Cu}=\frac{141560}{25\times 386}=14.7 kg$

Hence, the mass of copper bowl=14.7 kg

Option D is true.