It takes 45.0 J to raise the temperature of an 9.70 g piece of unknown metal from 13.0 degrees C to 24.5 degreesC. What is the specific heat for the metal?

q = mass metal x specific heat metal x delta T.

Solve for specific heat metal, the only unknown.

To find the specific heat of the metal, we can use the formula:

q = m * c * ΔT

Where:
q is the heat energy absorbed by the metal,
m is the mass of the metal,
c is the specific heat of the metal,
ΔT is the change in temperature.

In this case, we are given:
q = 45.0 J
m = 9.70 g (which we need to convert to kg)
ΔT = 24.5 °C - 13.0 °C

First, let's convert the mass from grams to kilograms:
m = 9.70 g ÷ 1000 = 0.00970 kg

Next, let's calculate the change in temperature:
ΔT = 24.5 °C - 13.0 °C = 11.5 °C

Now we can rearrange the formula to solve for c:
c = q / (m * ΔT)

Plugging in the given values:
c = 45.0 J / (0.00970 kg * 11.5 °C)

Let's calculate the specific heat for the metal: