Specific heat and heat capacity – problems and solutions

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

Known :

Mass (m) = 2 kg = 2000 gr

Heat (Q) = 100 cal

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

Wanted : The specific heat (c)

Solution :

c = Q / m ΔT

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

c = 100 cal / 100,000 gr ^oC

c = 10² cal / 10⁵ gr ^oC

c = (10² cal)(10^-5 gr^{-1 o}C^-1)

c = 10^-3 cal gr^{-1 o}C^-1

c = 10^-3 cal/gr ^oC

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

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

Known :

The specific heat (c) = 4180 J/kg C^o

Mass (m) = 2 kg

Wanted : Heat capacity (C)

Solution :

C = m c

C = (2 kg)(4180 J/kg C^o)

C = (2)(4180 J/C^o)

C = 8360 J/C^o

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

Known :

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

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 C^o)

C = 18 x 10^-3 x 10² J/C^o

C = 18 x 10^-1 J/C^o

C = 1.8 J/C^o

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1. Converting temperature scales
2. Linear expansion
3. Area expansion
4. Volume expansion
5. Heat
6. Mechanical equivalent of heat
7. Specific heat and heat capacity
8. Latent heat, heat of fusion, heat of vaporization
9. Energy conservation for heat transfer