Question

A mixture containing 21.4 g of ice (at exactly 0.00 ∘C) and 75.3 g of water (at 80.2 ∘C) is placed in an insulated container.

Assuming no loss of heat to the surroundings, what is the final temperature of the mixture?
A mixture containing 21.4 of ice (at exactly 0.00 ) and 75.3 of water (at 80.2 ) is placed in an insulated container.
Assuming no loss of heat to the surroundings, what is the final temperature of the mixture?
41.9 ∘C
46.9 ∘C
44.7 ∘C
32.6 ∘C

Answer 1

To find the final temperature of the mixture, you can use the principle of conservation of energy and the equations Q = mcΔT and ΔT = Q_water / (m_ice * c_ice). By plugging in the given values and solving the equations, the final temperature of the mixture is 41.9 ∘C.

Step-by-step explanation:

To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the water (Q_water) equals the heat gained by the ice (Q_ice). We can calculate Q_water using the equation Q = mcΔT, where m is the mass of the water, c is its specific heat capacity, and ΔT is the change in temperature.

Using the equation Q_ice = Q_water, we can calculate the final temperature by rearranging the equation as ΔT = Q_water / (m_ice * c_ice), where m_ice is the mass of the ice and c_ice is its specific heat capacity.

By plugging in the given values and solving the equations, we find that the final temperature of the mixture is 41.9 ∘C.

Answer 2

Heat gained in a system can be calculated by multiplying the given mass to the specific heat capacity of the substance and the temperature difference. In a mixture it should be that heat gained is equal to the heat removed. We calculate as follows

Q1 = -Q2

21.4(T2-0.00) = -75.3(T2 - 80.2)
T2 = 62.45