If 1.38 g of steam at 100.0°C condenses into 38.6 g of water, initially at 27.6°C, in an insulated container, what is the final temperature of the entire water sample? Assume no loss of heat into the surroundings.

Question

If 1.38 g of steam at 100.0°C condenses into 38.6 g of water, initially at 27.6°C, in an insulated container, what is the final temperature of the entire water sample? Assume no loss of heat into the surroundings.

°C

Answer 1

To find the final temperature of the entire water sample, we can use the principle of conservation of energy, specifically the concept of heat transfer.

First, let's break down the energy changes that occur in this process:

1. Heat lost by steam: The steam initially at 100.0°C condenses into water at a lower temperature. This heat transfer can be calculated using the formula:

Q1 = m1 * c1 * (T1 - T2)

Where:
Q1 = Heat lost by steam
m1 = Mass of steam (1.38 g)
c1 = Specific heat capacity of steam (we'll assume it is approximately the same as water, which is 4.18 J/g°C)
T1 = Initial temperature of steam (100.0°C)
T2 = Final temperature of water sample

2. Heat gained by water: The water initially at 27.6°C absorbs the heat transferred from the steam, causing its temperature to rise. This heat transfer can be calculated similarly:

Q2 = m2 * c2 * (T2 - T3)

Where:
Q2 = Heat gained by water
m2 = Mass of water (38.6 g)
c2 = Specific heat capacity of water (4.18 J/g°C)
T3 = Initial temperature of water (27.6°C)

3. Total heat transfer: Since the process is insulated (no heat loss to the surroundings), the heat lost by steam is equal to the heat gained by water. Therefore, we can equate Q1 and Q2:

Q1 = Q2
m1 * c1 * (T1 - T2) = m2 * c2 * (T2 - T3)

Now, we can substitute the given values into the equation and solve for T2:

1.38 g * 4.18 J/g°C * (100.0°C - T2) = 38.6 g * 4.18 J/g°C * (T2 - 27.6°C)

Simplify the equation:

5.7652 g°C * (100.0°C - T2) = 160.628 g°C * (T2 - 27.6°C)

Divide both sides by (100.0°C - T2) and (T2 - 27.6°C):

5.7652 g°C / (100.0°C - T2) = 160.628 g°C / (T2 - 27.6°C)

Cross multiply:

5.7652 g°C * (T2 - 27.6°C) = 160.628 g°C * (100.0°C - T2)

Simplify and rearrange the equation:

5.7652 T2 - 159.19032 = 16062.8 - 160.628 T2

Combine like terms:

166.3932 T2 = 16222.99032

Solve for T2:

T2 = 16222.99032 / 166.3932

T2 ≈ 97.63°C

Therefore, the final temperature of the entire water sample is approximately 97.63°C.

If 1.38 g of steam at 100.0°C condenses into 38.6 g of water, initially at 27.6°C, in an insulated container, what is the final temperature of the entire water sample? Assume no loss of heat into the surroundings.

3.31

To find the final temperature of the entire water sample, we can use the principle of conservation of energy, specifically the concept of heat transfer.