How Much Steam is Needed to Raise Water Temperature from 20°C to 50°C?

[cogs24]

hi guys, i have the following question to answer:

a 40g copper calorimeter contains 200g of water at 20 degrees celsius, it asks how much stam must be condensed in order to achieve a final temperature of 50 degrees celsius.
I was just wondering what formula to use?, and do i need to know the specific heat of copper?

 

[russ_watters]

Yes, using the specific heat of copper and water, calculate how much heat is gained as the temperature rises from 20 to 50C. The equation for the calorimeter is simply heat gain equals specific heat times delta-T. For condesing steam, you have two parts: the heat loss from condensing the steam and the heat loss from cooling it from 100C to 50C.

 

[thepatientmental]

To answer this question, we can use the formula for heat transfer: Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.

In this case, we are trying to find the amount of steam (Q) needed to achieve a final temperature of 50 degrees Celsius. We know the mass of water (200g) and the change in temperature (50-20 = 30 degrees Celsius). We also need to know the specific heat of water, which is 4.186 J/g°C.

However, we do not need to know the specific heat of copper in this case because the calorimeter is not involved in the heat transfer process. It is simply used to contain the water.

So, we can set up the equation as follows:

Q = (200g)(4.186 J/g°C)(30°C)
Q = 25,116 J

This is the amount of heat needed to raise the temperature of the water from 20 degrees Celsius to 50 degrees Celsius. Now, we need to convert this heat into the amount of steam needed.

We can use the formula for heat of vaporization: Q = mL, where Q is the heat transferred, m is the mass, and L is the heat of vaporization.

In this case, we know the heat of vaporization of water is 2260 J/g. So, we can rearrange the equation to solve for mass:

m = Q/L
m = (25,116 J)/(2260 J/g)
m = 11.11 g

Therefore, 11.11 grams of steam must be condensed in order to achieve a final temperature of 50 degrees Celsius. I hope this helps!