Question

The amount of heat (q) gained or lost by a substance (with mass m) as its temperature changes (ΔT) depends on its specific heat capacity (Cp) according to the following equation. q = Cp ✕ m ✕ ΔT The quality of industrial diamonds is determined in part by measuring the specific heat capacity, which is 0.5091 J/g·K for pure diamond. If the absorption of 26.21 J of heat by a 2.03 g diamond sample of unknown purity causes its temperature to rise from 25.99°C to 73.81°C, is the diamond sample pure? Explain your reasoning.

Answer 1

Answer:

As the specific heat capacity for pure diamond is 0.5091$\frac{J}{g.K}$ and it is different from the specific heat capacity found that is 0.2699$\frac{J}{g.K}$, the diamond sample is not pure.

Explanation:

1. As the problem says the equation that describes the amount of heat gained or lost by a substance is:

$q=Cp*m*(T_{2}-T_{1})$

q=Cp*m*ΔT

where q is the amount of heat, Cp is the specific heat capacity, m is the mass and ΔT is the change in the temperature.

2. Solving for specific heat capacity:

$Cp=\frac{q}{m*(T_{2}-T_{1})}$

3. Replacing values:

$Cp=\frac{26.21J}{2.03g*(73.81C-25.99C}$

$Cp=0.2699\frac{J}{g.K}$

As the specific heat capacity for pure diamond is 0.5091$\frac{J}{g.K}$ and it is different from the specific heat capacity found that is 0.2699$\frac{J}{g.K}$, the diamond sample is not pure.