Determine the specific heat of unknown metal from the fact that 6.40 * 10-2kj are needed to raise the temperature of 15g of unknown metal from 22 degrees Celsius to 33 degrees Celsius?

Question

Avery Adams · Accepted Answer

#c=3.88 * 10^-4 "kJ"/("g"*"degC")#

#c = 0.388 "J"/("g"*"degC")# Let's start with the equation #Q=mcDeltaT# We know #Q#, #m#, and #DeltaT#, we just need to find #c#, so with some rearranging: #c = Q/(m*DeltaT)# Now we plug everything we know from the equation in: #c= (6.40 * 10^-2 "kJ")/(15 "g" * (33 "degC" - 22 "degC"))# #c= (6.40 * 10^-2 "kJ")/(15 "g" *(11 "degC"))# #c=3.88 * 10^-4 "kJ"/("g"*"degC")# #c = 0.388 "J"/("g"*"degC")# Hope this helps!

Naomi Aronson · Answer

undefined To determine the specific heat ($ c $) of the unknown metal, you can use the formula:

$$
q = m \times c \times \Delta T
$$

Where:
$ q $ = heat energy (in joules)
$ m $ = mass of the metal (in grams)
$ c $ = specific heat of the metal (in $ \text{J/g°C} $)
$ \Delta T $ = change in temperature (in °C)

Given:
$ q = 6.40 \times 10^{-2} \text{ kJ} = 6.40 \times 10^{-2} \times 10^3 \text{ J} = 64 \text{ J} $
$ m = 15 \text{ g} $
$ \Delta T = 33°C - 22°C = 11°C $

Substituting these values into the formula:

$$
64 \text{ J} = 15 \text{ g} \times c \times 11°C
$$

Solving for $ c $:

$$
c = \frac{64 \text{ J}}{15 \text{ g} \times 11°C} = \frac{64}{165} \text{ J/g°C} \approx 0.387 \text{ J/g°C}
$$

The specific heat of the unknown metal is approximately $ 0.387 \text{ J/g°C} $.