The starship enterprise is caught in a time warp and spock is forced to use the primitive techniques of the 20th century to determine the specific heat capacity of an unknown mineral. the 128-g sample was heated to 96.2°c and placed into a calorimeter containing 77.2 g of water at 20.0°c. the heat capacity of the calorimeter was 13.9 j/k. the final temperature in the calorimeter was 23.3°c. what is the specific heat capacity (in j/g°c) of the mineral? enter to 4 decimal places.

Explanation:

The heat released by the unknown mineral (, where we will use the minus sign to indicate release of heat) is the heat absorbed by the calorimeter with water , so we can write:

The formula that relates heat with the mass of a material, its specific heat capacity and the temperature difference it suffers because of that heat is:

So we substitute this into the previous equation to get:

Since at the end the final temperatures will be the same, namely

We can write

Since what we want is the specific heat capacity of the unknown mineral , we can write:

In this particular equation it is not necessary to transform g to Kg (since the units of masses are cancelling out) or Celsius to Kelvin (since temperature is only appearing as a difference), but if one is not sure, the units should be transformed to S.I. since Joules is in S.I.

Finally then we have:

Since it asks for 4 decimal places, this must be written as:

the device is called “ rocket engine”