Specific heat and heat capacity – problems and solutions

1. A body with mass 2 kg absorbs heat 100 calories when its temperature raises from 20oC to 70oC. What is the specific heat of the body?

Known :

Mass (m) = 2 kg = 2000 gr

Heat (Q) = 100 cal

The change in temperature (ΔT) = 70oC – 20oC = 50oC

Wanted : The specific heat (c)

Solution :

c = Q / m ΔT

c = 100 cal / (2000 gr)(50oC)

c = 100 cal / 100,000 gr oC

c = 102 cal / 105 gr oC

c = (102 cal)(10-5 gr-1 oC-1)

c = 10-3 cal gr-1 oC-1

c = 10-3 cal/gr oC

The specific heat of the body is 10-3 cal/gr oC

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2. The specific heat of water is 4180 J/kg Co. How much the heat capacity of 2 kg water…

Known :

The specific heat (c) = 4180 J/kg Co

Mass (m) = 2 kg

Wanted : Heat capacity (C)

Solution :

C = m c

C = (2 kg)(4180 J/kg Co)

C = (2)(4180 J/Co)

C = 8360 J/Co

3. The specific heat of aluminum is 900 J/kg Co. How much the heat capacity of 2 gram aluminum…..

Known :

The specific heat of aluminum (c) = 900 J/kg Co = 9 x 102 J/kg Co

Mass (m) = 2 gram = 2/1000 kg = 2/103 kg = 2 x 10-3 kg

Wanted : Heat capacity (C)

Solution :

C = m c

C = (2 x 10-3 kg)(9 x 102 J/kg Co)

C = 18 x 10-3 x 102 J/Co

C = 18 x 10-1 J/Co

C = 1.8 J/Co

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