Question

The optimum drinking temperature for a Shiraz is 15.0 ∘C . A certain bottle of Shiraz having a heat capacity of 3.40 kJ∘C−1 is 23.1 ∘C at room temperature. The heat of fusion of ice is 6.02 kJmol−1 and the heat capacity of ice is 2.108 Jg−1∘C−1. Assume that no heat is lost to the rest of the surroundings. What minimum mass of ice, originally at -5.0 ∘C , is required to bring the final temperature to 15.0 ∘C ?

Answer 1

We have that the  minimum mass of ice , required to bring the final temperature to 15.0 ∘C is mathematical given as

• m=67.9g

From the question we are told

• The optimum drinking temperature for a Shiraz is 15.0 ∘C .
• A certain bottle of Shiraz having a heat capacity of 3.40 kJ∘C−1 is 23.1 ∘C at room temperature.
• The heat of fusion of ice is 6.02 kJmol−1 and the heat capacity of ice is 2.108 Jg−1∘C−1.

Heat released

Generally the equation for the Heat released   is mathematically given as

Q=cDT

Q=3.4*8.1*10^3

Q=27540J

Therefore

Heat absorded

H=m*4*2.108+m/18*6.02*10^3+m*15*4.18

H=405.58mJ

THerefore

• $m=\frac{27540J}{405.58}$

m=67.9g

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