30. A 0.035-kg ice cube at -30.0 C is placed in 0.33 kg of 35.0 C water in a very well-insulated container. The latent heat of fusion for water is Lf=79.8 kcal/kg.
What is the final temperature of the water, in degrees Celsius?
first, we need to take ice from -30 C to 0 C then melt it to water
so,
Q = mcT + mLf
where, m is mass of ice .
this must be equal to heat lost by water
mcT + mLf = -M * c * Tw
mcT + mLf = -M * c * (Tf - Ti)
put the values now, we get
0.035 * 2090 * 30 + 0.035 * 334e3 = -0.33 * 4186 * (Tf - 35)
solve for Tf
Tf = 24.95 C
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