Question

The temperature of 600 g of cold water rises by ${{15}^{0}}$, when 300 g of water ${{50}^{0}}$ is added to it. What is the initial temperature of the cold water?

A.${{10}^{0}}C$
B.${{15}^{0}}C$
C.${{5}^{0}}C$
D.${{25}^{0}}C$

Answer 1

Hint: Study about the heat transfer from objects. Learn about the specific heat capacity and try to obtain the formulas. Then we can solve this question.
Formula used:

$Q=mc\Delta T$

Complete step by step answer:
Heat transferred to an object from another object can be given by,

$Q=mc\Delta T$

Where, Q is the heat transferred, m is the mass of the object, c is the specific heat capacity of the material and $\Delta T$ is the change in temperature due to heat transfer.

It is given that the temperature of 600 g of cold water rises by ${{15}^{0}}$, when 300 g of water at a temperature ${{50}^{0}}$ is added to it.

So, Heat gained by cold water is equal to the heat lost by hot water.

$\begin{aligned} & \text{Heat gained }=\text{ Heat lost} \\\ & mc\Delta T={m}'c\Delta {T}' \\\ \end{aligned}$

Where m is the mass of cold water and $\Delta T$is the change in temperature of the cold water; ${m}'$ is the mass of hot water and $\Delta {T}'$ is the change in temperature of the hot water.

Let, the final temperature is ${{\text{T}}_{f}}$.
Now,

$\begin{aligned} & mc\Delta T={m}'c\Delta {T}' \\\ & m\Delta T={m}'\Delta {T}' \\\ & 600\times 15=300\times \left( 50-{{T}_{f}} \right) \\\ & 50-{{T}_{f}}=\dfrac{600\times 15}{300} \\\ & {{T}_{f}}=50-30 \\\ & {{T}_{f}}=20 \\\ \end{aligned}$

Hence, the final temperature is ${{T}_{f}}={{20}^{0}}C$

Now, the temperature rises by ${{15}^{0}}C$ to the final temperature ${{20}^{0}}C$.
So,

$\begin{aligned} & {{T}_{i}}+{{15}^{0}}C={{20}^{0}}C \\\ & {{T}_{i}}={{20}^{0}}C-{{15}^{0}}C \\\ & {{T}_{i}}={{5}^{0}}C \\\ \end{aligned}$

Here, ${{T}_{i}}$ is the initial temperature of the cold water.
So, the initial temperature is ${{5}^{0}}C$
The correct option is C.

Note: Heat capacity of an object can be defined as the heat required to rise the temperature of an object by 1 kelvin.
Specific heat capacity is the heat required to raise the temperature of an object of unit mass by 1 kelvin.