A student takes a calorimeter of mass `50 g`, made of copper of specific heat `0.1 "cal" g^(-1) C^(@ - 1)`. He puts 100g of water at `40^(@)C` into it. He drops 100g of ice at `- 20^(@)C` into it. He then passes steam so that water starts boiling. Latent heat of fussion is 80 cal/g and of vapourization is `540` cal/g. Specific heat of ice is `0.5 "cal" g^(-1) C^(@ - 1)`
Mass of steam required to raise the temperature of water to boil at `100^(@)C`

Options

A. `42.5g`
B. `44.35g`
C. `43.45g`
D. `46.84 g`

Answer

D

Explanation

We need the total system to be at `100^(@)C`

`{:(Q_(1) = 100 xx 0.5 xx 20,Q_(2) = m xx L,),(Q_(1) 1000 "cal",Q_(2) = 8000 "cal",):}`
In which water and calorimeter can provide
`= m_(w) xx s_(w) xx (Delta T)_(w) + m_(C) xx s_(C) xx (Delta T)_(C)`
`= 100 xx 1 (40) + 50 xx 0.1 (40) = 4200` cal.
i.e. we need an extra 4800 cal heat.
`{:((Q)_("supplied b steam"),= m_(w) xx s_(w) xx (Delta T),),(,+ m_(C) s_(C) xx (Delta T)_(c) + (Q)_("extra"),):}`
`= 200 xx 1 xx (100) + 50 xx 0.1 (100) + 4800`
`(m)_("steam") xx 540 = 20000 + 500 + 4800`
`(m)_("steam") = 46.85` grams.