Find what heat is required to change 17 g of 14 ∘C water to 100∘C steam. Express your answer in calories.

Oh boy, we're turning up the heat here! Alright, let's calculate the heat required to transform 17 g of water from 14 ∘C to 100∘C.

To do that, we need to consider two steps: raising the temperature from 14 ∘C to 100∘C (heating), and then turning the water into steam (vaporization).

First, let's calculate the heat required for heating the water. The specific heat capacity of water is about 1 calorie per gram per degree Celsius. So, to raise the water's temperature by 86 degrees (100∘C - 14∘C), we'll need:

Q = m * c * ΔT
Q = 17 g * 1 cal/g∘C * 86∘C
Q = 1462 cal

Now, for the vaporization part. The heat of vaporization for water is about 540 calories per gram. Since we have 17 grams of water, the heat required will be:

Q = m * H
Q = 17 g * 540 cal/g
Q = 9180 cal

Finally, to find the total heat required, we simply add up the two calculated values:

Total heat = Heating heat + Vaporization heat
Total heat = 1462 cal + 9180 cal
Total heat = 10642 cal

So, to change 17 g of 14 ∘C water to 100∘C steam, we'll need a total of approximately 10642 calories. Now that's a hot transformation, isn't it?

To calculate the heat required to change the temperature of water from 14 ∘C to 100∘C, we need to consider two separate processes: heating the water from 14 ∘C to 100∘C, and then converting the 100∘C water to steam.

Step 1: Heat required to raise the temperature from 14 ∘C to 100∘C:
The specific heat capacity of water is 1 cal/g⋅∘C.
The formula to calculate the heat required is:
Q = m * c * ΔT
where:
Q is the heat required (in calories)
m is the mass of water (in grams)
c is the specific heat capacity of water (in cal/g⋅∘C)
ΔT is the change in temperature (in ∘C)

Q1 = 17 g * 1 cal/g⋅∘C * (100∘C - 14∘C)
= 17 g * 1 cal/g⋅∘C * 86∘C
= 1462 cal

So, the heat required to raise the temperature of 17 g of water from 14 ∘C to 100∘C is 1462 calories.

Step 2: Heat required to convert the 100∘C water to steam:
The heat of vaporization of water is 540 cal/g.

The formula to calculate the heat required is:
Q = m * Hv
where:
Q is the heat required (in calories)
m is the mass of water (in grams)
Hv is the heat of vaporization of water (in cal/g)

Q2 = 17 g * 540 cal/g
= 9180 cal

So, the heat required to convert 17 g of 100∘C water to steam is 9180 calories.

Step 3: Total heat required:
To find the total heat required, we add Q1 and Q2 together:

Total heat required = Q1 + Q2
Total heat required = 1462 cal + 9180 cal
Total heat required = 10642 cal

Therefore, the heat required to change 17 g of 14 ∘C water to 100∘C steam is 10642 calories.

To find the heat required to change the temperature of water from 14 ∘C to 100 ∘C, we need to consider two parts:

1. Heating the water from 14 ∘C to 100 ∘C
2. Changing the water at 100 ∘C to steam at the same temperature.

Let's calculate these parts step by step:

1. Heating the water to 100 ∘C:
The specific heat capacity of water is 1 cal/g ∘C, which means it takes 1 calorie of heat to raise the temperature of 1 gram of water by 1 ∘C.

Given:
Mass of water (m) = 17 g
Initial temperature (T1) = 14 ∘C
Final temperature (T2) = 100 ∘C
Specific heat capacity of water (c) = 1 cal/g ∘C

We need to calculate the heat required to raise the temperature of the water:

Heat (Q1) = m * c * (T2 - T1)
= 17 g * 1 cal/g ∘C * (100 ∘C - 14 ∘C)

Calculating this will give us the heat required to heat the water to 100 ∘C.

2. Changing water to steam at 100 ∘C:
To change water at its boiling point (100 ∘C) to steam at the same temperature, we need to consider the heat of vaporization.

The heat of vaporization of water is approximately 540 cal/g. This means it takes 540 calories to convert 1 gram of water at 100 ∘C to steam at the same temperature.

Given:
Mass of water (m) = 17 g
Heat of vaporization (Hv) = 540 cal/g

We need to calculate the heat required to change the water to steam:

Heat (Q2) = m * Hv
= 17 g * 540 cal/g

Adding Q1 and Q2 will give us the total heat required to change 17 g of 14 ∘C water to 100 ∘C steam:

Total Heat = Q1 + Q2

Finally, calculate the value to get the answer in calories.

17 * (specific heat of water) * (100 - 14) + 17* (heat of vaporization of water)