# 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^{o}C to 70^{o}C. 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^{o}C – 20^{o}C = 50^{o}C

__Wanted :__ The specific heat (c)

__Solution :__

c = Q / m ΔT

c = 100 cal / (2000 gr)(50^{o}C)

c = 100 cal / 100,000 gr ^{o}C

c = 10^{2} cal / 10^{5} gr ^{o}C

c = (10^{2} cal)(10^{-5} gr^{-1} ^{o}C^{-1})

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

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

The specific heat of the body is 10^{-3 }cal/gr ^{o}C

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 10^{2} J/kg C^{o }

Mass (m) = 2 gram = 2/1000 kg = 2/10^{3} kg = 2 x 10^{-3 }kg

__Wanted :__ Heat capacity (C)

__Solution :__

C = m c

C = (2 x 10^{-3 }kg)(9 x 10^{2} J/kg C^{o})

C = 18 x 10^{-3 }x 10^{2} J/C^{o}

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

C = 1.8 J/C^{o}

- Converting temperature scales
- Linear expansion
- Area expansion
- Volume expansion
- Heat
- Mechanical equivalent of heat
- Specific heat and heat capacity
- Latent heat, heat of fusion, heat of vaporization
- Energy conservation for heat transfer