Question

If you pour 0.0100 kg of 20.0ºC water onto a 1.20-kg block of ice (initially at −15.0ºC), what is the final temperature?

a) -12.5ºC
b) -10.0ºC
c) -7.5ºC
d) -5.0ºC

Answer 1

The final temperature is approximately -12.41 °C.

Step-by-step explanation:

To find the final temperature, we need to consider the heat gained by the ice and the heat lost by the water. The formula to determine the final temperature is:

mcΔT = mcΔT

Where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Since the water cools so rapidly, we can assume that the heat lost by the water is equal to the heat gained by the ice.

Using the formula, we can calculate the final temperature:

(0.0100 kg)(4,186 J/kg°C)(T - 20.0°C) = (1.20 kg)(2,093 J/kg°C)(T + 15.0°C)

Let's solve for T:

0.0100(4,186)(T - 20.0) = 1.20(2,093)(T + 15.0)

41.86T - 837.2 = 2,511.6T + 31,494

-2,469.6T = -30,657.2

T ≈ -12.41 °C

So, the final temperature is approximately -12.41°C.