Question

# You pour 200 g hot coffee at 78.7°C and some cold cream at 7.50°C to a...

You pour 200 g hot coffee at 78.7°C and some cold cream at 7.50°C to a 115-g cup that is initially at a temperature of 22.0°C. The cup, coffee, and cream reach an equilibrium temperature of 62.0°C. The material of the cup has a specific heat of 0.2604 kcal/(kg · °C) and the specific heat of both the coffee and cream is 1.00 kcal/(kg · C). If no heat is lost to the surroundings or gained from the surroundings, how much cream did you add?

The overall change in energy must be 0.

Change in energy of the coffee

= (0.200 kg) * (62.0 - 78.7 C°) * (1.00 kcal/(kg C°) )

= -3.34 kcal

Change in energy of the cream

= (x kg) * (62.0 - 7.50 C°) * (1.00 kcal/(kg C°) )

= 54.5x kcal

Change in energy of the cup

= (0.115 kg) * (62.0 - 22.0 C°) * (0.2604 kcal/(kg C°))

= 1.19784 kcal

If we add them up, the sum should be 0 (since no heat was lost to the surroundings):

-3.34 + 54.5x + 1.19784 = 0

x = 0.0393

x = 0.039 ( appprox)

Therefore, the amount of cream was

x = 0.039kg = 39 g

I hope this will help you. Have a good day. Please give a like. Its very important. Thanks.