Anonymous
Anonymous asked in Science & MathematicsChemistry · 2 months ago

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).

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  • 2 months ago
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    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.

    High  five!!

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