Question

A 52.9g sample of brass, which has a specific heat capacity of 0.375·J·g^−1°C^−1, is put into a calorimeter (see sketch at right) that contains 100.0g of water. The temperature of the water starts off at 15.0°C. When the temperature of the water stops changing it's 18.4°C. The pressure remains constant at 1 atm. Calculate the initial temperature of the brass sample.

Answer 1

Answer: 90.04°C

Explanation: Calorimeter is a device measures the amount of heat of a chemical or physical process. An ideal calorimeter is one that is well-insulated, i.e., prevent the transfer  of heat between the calorimeter and its surroundings. So, the net heat change inside the calorimeter is zero:

$q_{1}+q_{2}=0$

Rearraging, it can be written as

$q_{1}=-q_{2}$

showing that the heat gained by Substance 1 is equal to the energy lost by Substance 2.

In our case, water is gaining heat, because its temperature has risen and so, brass is losing energy:

$q_{water}=-q_{brass}$

Calculating:

$m_{w}.c_{w}.\Delta T=-[m_{b}.c_{b}.\Delta T]$

$100.4.18.(18.4-15)=-[52.9.0.375.(18.4-T)]$

Note: final temperature is the same as the substances are in thermal equilibrium.

Solving:

418(3.4)= - 365.01 + 19.8375T

19.8375T = 1786.21

T = 90.04

The initial temperature for the sample of brass was 90.04°.