The same amount of heat entering identical masses of different substances produces different temperature changes. Calculate the final temperature when 1.50 kcal of heat enters 1.25 kg of the following, originally at 22.5°C.

3edx

21.0 degrees celcius

To calculate the final temperature when a certain amount of heat enters a substance, we need to use the formula:

Q = mcΔT

where Q is the amount of heat, m is the mass of the substance, c is its specific heat capacity, and ΔT is the change in temperature.

First, let's determine the specific heat capacity (c) of the substance. The specific heat capacity is the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius.

Since we have different substances, we need to look up their specific heat capacities. For example, the specific heat capacity of water is approximately 4.18 J/g°C, while the specific heat capacity of aluminum is about 0.897 J/g°C.

Now, let's calculate the final temperature for each substance.

For water:
Given:
Q = 1.50 kcal = 1.50 * 10^3 cal (since 1 kcal = 1000 cal)
m = 1.25 kg
ΔT = final temperature - initial temperature

Using the formula Q = mcΔT, we rearrange the equation to solve for ΔT:
ΔT = Q / (mc)

Converting the mass to grams (1.25 kg = 1250 g), and converting calories to joules (1 cal = 4.18 J):
ΔT = (1.50 * 10^3 cal) / (1250 g * 4.18 J/g°C)
ΔT = (1.50 * 10^3) / (1250 * 4.18) °C
ΔT ≈ 0.286 °C

Now we can calculate the final temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 22.5°C + 0.286°C
Final temperature ≈ 22.79°C

Therefore, when 1.50 kcal of heat is applied to 1.25 kg of water initially at 22.5°C, the final temperature is approximately 22.79°C.

Repeat the same calculation for other substances considering their specific heat capacities to find their final temperatures.