Question

Suppose that 50 g of water at 32 ºC is poured into a 70-g aluminum cup with an initial temperature of 11 ºC. The final temperature of the system will be:

Answer 1

Answer:

The final temperature of the system is 27.14°C.

Explanation:

Given that,

Mass of water = 50 g

Temperature = 32°C

Mass of aluminum = 70 g

Temperature = 11°C

Let T be the final temperature of the system

Heat loss by the water

$Q_{w}=m_{w}c_{w}(T_{1}-T)$

Heat gained by the aluminum

$Q_{a}=m_{a}c_{a}(T-T_{2})$

We need to calculate the final temperature of the system

Heat loss by the water = Heat gained by the aluminum

$m_{w}c_{w}(T_{1}-T)=m_{a}c_{a}(T-T_{2})$

$T=\dfrac{m_{w}c_{w}T_{1}+m_{a}c_{a}T_{2}}{m_{a}c_{a}+m_{w}c_{w}}$

Put the value into the formula

$T=\dfrac{50\times10^{-3}\times4186\times32+70\times10^{-3}\times900\times11}{50\times10^{-3}\times4186+70\times10^{-3}\times900}$

$T=27.14^{\circ}C$

Hence, The final temperature of the system is 27.14°C.