Question

I place an ice cube with a mass of 0.223 kg and a temperature of −35◦C is placed into an insulated aluminum container with a mass of 0.553 kg containing 0.452 kg of water. The water and the container are initially in thermal equilibrium tatemperature of 27◦C. Assumingthatnoheatentersorleavesthe System,whatwillthefinaltemperature of the system be when it reaches equilibrium, and how much ice will be in the container when it reaches equilibrium

Answer 1

To solve this problem it is necessary to use the calorimetry principle. From the statement it asks about the remaining ice, that is, to the point where the final temperature is 0 ° C.

We will calculate the melted ice and in the end we will subtract the total initial mass to find out how much mass was left.

The amount of heat transferred is defined by

$Q = mc\Delta T$

Where,

m = mass

c = Specific heat

$\Delta T =$Change in temperature

There are two states, the first is that of heat absorbed by that mass 'm' of melted ice and the second is that of heat absorbed by heat from -35 ° C until 0 ° C is reached.

Performing energy balance then we will have to

$Q_i-E_h = Q_m$

Where,

$Q_ i$= Heat absorbed by whole ice

$Q_m$= Heat absorbed by mass

$E_h$= Heat energy by latent heat fusion/melting

$m_i*c_i \Delta T +m*L_f = (m_wc_w+m_{al}c_{al})\Delta T$

Replacing with our values we have that

$0.223*2108(-(-35))+m*3.34*10^5 = (0.452*4186+0.553*902)(27-0)$

$16452.9+334000m = (1892.072+498.806)*27$

Rearrange and find m,

$m = 0.144Kg$

Therefore the Ice left would be

$m' = 0.223-0.144$

$m' = 0.079Kg$

Therefore there is 0.079kg ice in the containter when it reaches equilibrium