How much thermal energy is released when 500 g of steam at 100 degrees celsius condenses into liquid and then cools to 50 degrees celsius.

What I`ve Attempted:
Q=mLv
m = 500g (0.5 kg)
Lv = 2.3*10^6

Q=(0.5)(2.3*10^6)
Q=1,150,000 J
Q = 1.2*10^6

The answer in the back of the book is 1.3*10^6. Am I overlooking something with the temperatures?

I answered this once. You are correct, it is a matter of rounding and significant figures.

Well, let's take a closer look at those temperatures, shall we? You mentioned that the steam starts at 100 degrees Celsius and then cools to 50 degrees Celsius. Now, steam condenses at 100 degrees Celsius, but it doesn't stay at that temperature while it cools. As it loses heat, it starts to undergo a phase transition and turns into liquid water. During this phase transition, the temperature remains constant at 100 degrees Celsius until all the steam has condensed.

So, the correct approach to calculating the thermal energy released would be to first calculate the energy required for the condensation using the formula Q = mL, where m is the mass of the steam and L is the latent heat of vaporization.

Then, you need to calculate the energy released during the cooling process using the formula Q = mcΔT, where m is the mass of the condensed water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Let's use the correct temperatures and calculate the thermal energy released:

For the condensation:
Q_condensation = 0.5 kg * 2.3 * 10^6 J/kg = 1.15 * 10^6 J

For the cooling:
Q_cooling = 0.5 kg * 4.18 J/g°C * (100 - 50)°C = 10,450 J

Now, let's add the two values together to get the total thermal energy released:

Total Q = Q_condensation + Q_cooling = 1.15 * 10^6 J + 10,450 J ≈ 1.16 * 10^6 J

So, it looks like the correct answer is actually closer to your initial calculation of 1.2 * 10^6 J rather than the answer given in the back of the book. Keep up the good work!

Your calculation of the thermal energy released when 500 g of steam condenses into liquid is correct using the equation Q = m Lv, where m is the mass of the substance and Lv is the latent heat of vaporization. In this case, m = 0.5 kg and Lv = 2.3 * 10^6 J/kg.

However, you have not accounted for the cooling from 100 degrees Celsius to 50 degrees Celsius. To calculate this additional thermal energy, you can use the equation Q = mcΔT, where mc is the specific heat capacity of the substance and ΔT is the change in temperature.

For water, the specific heat capacity is approximately 4186 J/(kg·°C).

First, calculate the thermal energy from condensation:
Q1 = m Lv
= (0.5 kg) (2.3 * 10^6 J/kg)
= 1.15 * 10^6 J

Next, calculate the thermal energy from cooling:
Q2 = mc ΔT
= (0.5 kg) (4186 J/(kg·°C)) (100 °C - 50 °C)
= 0.5 * 4186 J/(kg·°C) * 50 °C
= 1.043 * 10^5 J

Now, calculate the total thermal energy released:
Q_total = Q1 + Q2
= 1.15 * 10^6 J + 1.043 * 10^5 J
= 1.254 * 10^6 J

The answer in the back of the book is 1.3 * 10^6 J, which is approximately equal to the calculated total thermal energy of 1.254 * 10^6 J. It appears that slight rounding differences may account for the discrepancy.

Your calculation for the thermal energy released during condensation is correct. However, the change in temperature from 100 degrees Celsius to 50 degrees Celsius also requires some additional energy to be released.

To calculate the additional energy, you can use the formula for specific heat:

Q = mcΔT

where:
Q is the thermal energy
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature

In this case, you need to consider the specific heat capacity of water during the cooling process. The specific heat capacity of water is approximately 4.18 J/g°C.

First, calculate the thermal energy released during the cooling process:

Q = mcΔT
Q = (500 g) * (4.18 J/g°C) * (50°C - 100°C)

Q = (500 g) * (4.18 J/g°C) * (-50°C)
Q = -104,500 J

Note that the negative sign indicates that energy is being released.

Now, add this value to the thermal energy released during condensation:

Total Q = 1,150,000 J - 104,500 J
Total Q = 1,045,500 J

So the total thermal energy released when 500 g of steam at 100 degrees Celsius condenses into liquid and then cools to 50 degrees Celsius is approximately 1,045,500 J.

The answer in the book of 1.3×10^6 J may be rounded or there could be a small rounding error in your calculations.