The mass of the block of ice is 2.24 kg
Explanation:
The amount of heat needed for the whole process consists of three different amounts of heat:
[tex]Q_1[/tex]: the amount of heat needed to raise the temperature of the block of ice from [tex]-10^{\circ}C[/tex] to [tex]0^{\circ}C[/tex]
[tex]Q_2[/tex]: the amount of heat needed to melt the block of ice at melting point
[tex]Q_3[/tex]: the amount of heat needed to raise the temperature of the water from [tex]0^{\circ}C[/tex] to [tex]11^{\circ}C[/tex]
The total amount of heat needed can be written as
[tex]Q=Q_1+Q_2+Q_3=mC_i\Delta T_1 + m\lambda_f + mC_w\Delta T_3[/tex]
where we have:
[tex]Q=9.0 \cdot 10^5 J[/tex] (total amount of heat required)
m is the mass of the block of ice
[tex]C_i = 2108 J/kg^{\circ}C[/tex] is the specific heat of ice
[tex]\lambda_f=3.34\cdot 10^5 J/kg[/tex] is the latent heat of fusion of ice
[tex]C_w=4186 J/kg^{\circ}C[/tex] is the specific heat capacity of water
[tex]\Delta T_1 = 0-(-10)=10^{\circ}C[/tex] is the change in temperature in the 1st process
[tex]\Delta T_3 = 11-0=11^{\circ}C[/tex] is the change in temperature in the 3rd process
Solving the equation for m, we find the mass of the block of ice:
[tex]m=\frac{Q}{C_i\Delta T_1 + \lambda_f+C_w\Delta T_3}=\frac{9.0\cdot 10^5}{(2108)(10)+3.34\cdot 10^5+(4186)(11)}=2.24 kg[/tex]
Learn more about specific heat capacity:
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