Calculating Water and Steam Temperatures

In summary, when calculating the total temperature of a mixture of water and steam, the energy lost by the steam as it condenses and cools must be equal to the energy gained by the water as it heats up. This can be found by using the idea of heat balance, where heat gained equals heat lost. This formula is a combination of mcΔT and mL, where mcΔT is used when there is a change in temperature and mL is used when there is a change in state. It is important to recognize individual heat sources and sinks and combine them to create the necessary formula.
  • #1
Asum
1
0
I'm looking at older exam questions.

If you mix 5 kg of water, with temperature 20 cel with 1kg of steam, with temperature 100 cel. What's the total temperature? (Cwater=4 kJ/kgK and r = 2 MJ/kg)

I don't know which formula to use to calculate it. Anyone know?

thx
 
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  • #2
Whatever the case is, the energy lost by the steam as it condenses and cools must be equal to the energy gained by the water as it heats up. You can use this idea to find the equilibrium temperature.
 
  • #3
Asum said:
I don't know which formula to use to calculate it. Anyone know?

Am I right assuming you think each question has its own magical formula, that you just have to plug numbers into get the final result? Well, that's wrong. The sooner you will accept the fact, the better for you.

In the case of heat balance questions only formula you need is heat gained = heat lost. But it is not a simple universal formula - you must be able to calculate heat gained and heat lost. It is always some combination of mcΔT (when substance changes temperature) and mL (when there is a change of state - vaporizing, melting, subliming). You have to be able to recognize individual heat sources and sinks, describe them using simple formulas, and combine them to get the formula you need. So you have to build your own formula from smaller formulas.
 

1. What is the formula for calculating water and steam temperatures?

The formula for calculating water and steam temperatures is T = (mL + cT1) / (m + c), where T is the final temperature, mL is the mass of liquid, c is the specific heat capacity, and T1 is the initial temperature.

2. What is the difference between water and steam temperatures?

The main difference between water and steam temperatures is their physical state. Water is a liquid at room temperature, whereas steam is a gaseous form of water at high temperatures. Water has a lower specific heat capacity compared to steam, meaning it takes less energy to increase its temperature.

3. How do you calculate the final temperature when mixing water and steam?

To calculate the final temperature when mixing water and steam, use the formula T = (m1T1 + m2T2) / (m1 + m2), where T is the final temperature, m1 and m2 are the masses of the water and steam respectively, and T1 and T2 are their initial temperatures.

4. How does pressure affect water and steam temperatures?

According to the ideal gas law, pressure and temperature are directly proportional. This means that an increase in pressure will result in an increase in temperature for both water and steam. However, steam has a higher boiling point than water, so it can exist at higher temperatures and pressures.

5. What factors can affect the accuracy of calculated water and steam temperatures?

The accuracy of calculated water and steam temperatures can be affected by several factors, including human error in measuring mass and temperature, variations in specific heat capacity due to impurities in the water, and changes in pressure or altitude. It is important to take these factors into account when performing calculations to ensure accurate results.

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