Question

ryan is a chemistry student that enjoys hot tea. he wants to determine how much ice is needed to cool 250.0 ml of tea to an optimal drinking temperature of 57.8 c. macmillan learning the method ryan uses to prepare his tea results in an initial temperature of 79.1 c. the average mass of an ice cube from the ice tray ryan uses is 18.8 g and has a starting temperature of - 8.33 deg * c assume that the heat capacity of tea is the same as pure water, and assume no heat is lost to the surroundings what mass of ice is needed to reach the optimal temperature of 57.8^ c^ prime ?

Answer 1

Ryan calculates that he requires 4 ice cubes for 250mL of hot tea to reach the optimal drinking temperature by using the specific heat capacity of tea.

A substance's potential to hold heat is indicated by its specific heat capacity. This substance size reflects the amount of heat required to raise a certain volume of a material's temperature by one Kelvin. Specific heat capacity is a distinguishing feature of every substance and is useful for material identification.

Given:

Final temperature of system is 57.8℃

dT1 = 79.1 - 57.8 = 21.3℃

dT2 = 0 - (-8.33) = 8.33℃

dT3 = 57.8 - 0 = 57.8℃

Mass of tea, m1 = 250.0mL = 250.0g = 0.250kg

Specific heat capacity of tea, C1 = 4186 J/kg℃ = Specific heat capacity of water

Specific heat capacity of ice, Ci = 2090 J/kg℃

Mass of each ice cubes, m of i = 18.8g

Latent heat of fusion of ice, Lf = 334 kJ/kg

To find:

No. of ice cubes required = ?

Calculations:

Suppose equilibrium temperature is T, then

Heat released by Tea = Heat gained by Ice

Q1 = Q2

m1x C1x dT1 = mi x Ci x dT2 + mi x Lf + mi x Cw x dT3

0.250x 4186 x 21.3 = mi x (2090 x 8.33 + 3.34 x $10^4$ + 4186 x 57.8)

mi = 0.250 x 4186 x 21.3 / (2090 x 8.33 + 3.34 x $10^4$ + 4186 x 57.8)

mi = 0.0761kg = 76.1g

Mass of ice required = 76.1g

Number of ice cube required will be:

n = Total mass of ice/mass of each ice cube

n = 76.1/18.8

n = 4.04 ice cubes = 4.0 ice cubes

Result:

Ryan requires 4 ice cubes to bring 250mL of hot tea to the optimal drinking temperature.

Learn more about Specific heat capacity here:

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