14.6k views
0 votes
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

User Surazzarus
by
7.1k points

1 Answer

6 votes

Answer:

D.14.7 kg

Step-by-step explanation:

Mass of block of ice=
m_i=400 g=400* 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* 10^3 Jkg


1KJ=1000 J

Latent heat of vaporization=
L_v=2256KJkg=2256* 10^3Jkg


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

Substitute the values


m_Cu* 386(30-5)=400* 10^(-3)* 333* 10^3+400* 10^(-3)* 4180(5-0)


m_(Cu)(25)(386)=141560


m_(Cu)=(141560)/(25* 386)=14.7 kg

Hence, the mass of copper bowl=14.7 kg

Option D is true.

User Sagar V
by
7.1k points