Question

A metallic spoon is placed in a hot cup of coffee. If the coffee gives away 190 calories to the spoon to cool down by 0.75°C, what is the mass of the coffee? (Assume that ccoffee = 1.0 cal/gC°.)

Answer 1

Taking into account the definition of calorimetry,  the mass of the coffee is 253.33 g.

Calorimetry

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).

So, the equation that allows to calculate heat exchanges is:

Q = c× m× ΔT

where:

• Q is the heat exchanged by a body of mass m.
• c is the specific heat sudstance.
• ΔT is the temperature variation.

Mass of coffee

In this case, you know:

• Q= 190 calories
• c= 1 $\frac{cal}{gC}$
• m= ?
• ΔT= 0.75 C

Replacing in the equation that allows to calculate heat exchanges is:

190 cal = 1 $\frac{cal}{gC}$× m× 0.75 C

Solving:

m= 190 cal÷ (1 $\frac{cal}{gC}$× 0.75 C)

m=253.33 g

Finally, the mass of the coffee is 253.33 g.

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