What mass of steam that is initially at 120 C is needed to warm 350g of water and its 300g aluminum container?

Question

What mass of steam that is initially at 120 C is needed to warm 350g of water and its 300g aluminum container from 20 C to 50 C?

Answer 1

Without knowing the steam pressure or knowing that there will not be condensation there is no one right answer.

Answer 2

We can assume that condensation and pressure are not an issue.

First calculate the amount of energy required to raise the temperature of the water and aluminum from 20 C to 50 C. This step can be done in Celsius or kelvin.

Multiply the heat capacity in J/gK by the mass in grams and the change in temperature. Do the water and aluminum separately then add the 2 together for a total.

(0.897 J/gK x 300 g x 30 C) + (4.1813 J/gK x 350 g x 30 C) = total joules required.

Take the total energy required (in Joules) and divide it by the heat capacity of steam then divide by the temperature of the steam (120 C). IMPORTANT!! The temperature of the steam must be converted to Kelvin for this step!! (Add 120 to 273.15)

(Total joules) J / 2.080 J/gK = ??? gK
??? gK / (120 +273.15) K = ??? grams

An important consideration for this type of thing is to do unit analysis. If you do the math on the units you can determine what your results might be or check if you have the right results. In the last step J divided by J/gK the joules cancel out and the gK winds up in the numerator (dividing is like multiplying by the inverse). Doing this can help with all calculations. If you need to calculate speed and you know distance traveled and the time you can confirm that you need to divide distance by time to get m/s.