Question

An 17.00 g cube of a metal was heated to 120.0 C and then plunged into 190.0 g of water at 24.0 C. The temperature of the resulting mixture became 28.0 C. Calculate the specific heat of the metal.

Answer 1

To calculate the specific heat of a metal, use the formula q = mcΔT for heat transfer and compare the result with known specific heats to determine the metal's identity. The specific heat calculation involves the heat absorbed or lost by water, the mass of the metal, and its temperature change.

Step-by-step explanation:

The question involves calculating the specific heat of a metal by using its mass, the change in its temperature, and the heat transferred, which is assumed to be absorbed or released by a quantity of water (calorimetry). The specific heat capacity (c) can be calculated using the formula q = mcΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Here are the steps to calculate the specific heat of the metal:

1. Calculate the heat absorbed or lost by water with the formula q = mcΔT. Assume water's specific heat is 4.184 J/g°C, which is a constant.
2. The heat gained by the water is equal to the heat lost by the metal when it is transferred into the water, under the assumption of no heat loss to the surroundings.
3. Use the heat calculated in step 1 and the mass and temperature change of the metal to find the metal's specific heat with the rearranged formula c = q / (mΔT).

By comparing the calculated specific heat with known specific heats of various metals, the identity of the metal can be predicted.