19 g of water at `30^@C` and 5 g of ice at `-20^@C` are mixed together in a calorimeter. What is the final temperature of the mixture? Given specific heat of ice `=0.5calg^(-1) (.^(@)C)^(-1)` and latent heat of fusion of ice `=80calg^(-1)`

Options

A. `0^@` C
B. `-5^@` C
C. `5^@ C`
D. `10^@ C`

Answer

C

Explanation

Heat loss by water = Heat gain by ice
`rArr m_(w)S_(w)(30-T) = m_i s_i[0-(-20)] + m_i xx L_f + m_i s_w (T-0)`
`rArr 19 xx 1 xx (30 - T) = 5xx0.5 xx 20 + 80 xx 5 + 5 xx 1 xx T`
`rArr T =(120)/(24) = 5^@C`.