To solve for the specific heat of the metal, we can use the equation:
heat lost by metal = heat gained by water
The heat lost by the metal can be calculated using the equation:
Q = m × c × ΔT
where:
m = mass of the metal (21.3 g)
c = specific heat of the metal (unknown)
ΔT = change in temperature of the metal (final temperature of water - initial temperature of metal)
ΔT = 24.0°C - 70.0°C = -46.0°C
Q = 21.3 g × c × (-46.0°C)
The heat gained by the water can be calculated using the equation:
Q = m × c × ΔT
where:
m = mass of the water (62.4 g)
c = specific heat of water (4.184 Jg^-1°C^-1)
ΔT = change in temperature of the water (final temperature - initial temperature)
ΔT = 24.0°C - 21.0°C = 3.0°C
Q = 62.4 g × 4.184 Jg^-1°C^-1 × 3.0°C
Since the heat lost by the metal is equal to the heat gained by the water, we can equate the two equations:
21.3 g × c × (-46.0°C) = 62.4 g × 4.184 Jg^-1°C^-1 × 3.0°C
Solving for c:
c = [62.4 g × 4.184 Jg^-1°C^-1 × 3.0°C] / [21.3 g × (-46.0°C)]
c ≈ 0.38 Jg^-1°C^-1
Therefore, the specific heat of the metal is approximately 0.38 Jg^-1°C^-1.