# Determine the amount of steam (in g) needed for the system to reach a final temperature of 48.0°C. ?

Steam at 100°C is condensed into a 38.0 g aluminum calorimeter cup containing 240 g of water at 21.0°C. Determine the amount of steam (in g) needed for the system to reach a final temperature of 48.0°C. The specific heat of aluminum is 900 J/(kg · °C).

### 1 Answer

- jacob sLv 72 months agoFavourite answer
The principle of Calorimetry is based on the fact that Energy can never be created nor destroyed.

In calorimeter,

Total energy released=Total energy used

Here, in this problem,

Energy will be released when steam is converted into water and that converted water

when come till 48 oC.

And energy will be used when temperature of water and brass increase to 48 oC

Let required mass of steam be Mx g.

We know Latent heat of vapourisation for water is 540 cal/gm i.e. 540 x 4.2 J/gm

Mass of brass = 38 gm=0.0038 kg

Latent heat of vaporization for water is 540 cal/gm , 540 x 4.2J/gm

Mass of Aluminium = 38 gm = 0.0038kg

E1 = 540 x 4.2J/gm = 2268Mx

Similarly , when water is 100 °C ( water from steam) goes to 48.0°C

E2 = Mx x (100 - 48) = 52Mx C = 52 x 4.2 x MxJ = 218.4MxJ

Energy used when water is 21.0°C goes to 48.0°C will be:

E3= 240 x 4.2(48 -21)J = 27216 J

E4 = 0.038 x 900 x (48 - 21 )J = 923.4J

Since energy used = energy released

So,

E1 + E2 = E3 + E4

Substituting

2268Mx + 218Mx = 27216 + 923.4

Mx(2268 + 218) = 28139.4

Mx = 28139.4/(2268 + 218)

Mx = 28139.4/(2486)

Mx = 11.32 gm

Hence mass of steam required is 11.32gm.

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