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).
- jacob sLv 72 months agoFavourite answer
The principle of Calorimetry is based on the fact that Energy can never be created nor destroyed.
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
E1 + E2 = E3 + E4
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.