Question

The water equivalent of copper calorimeter is 4.5 g. If specific heat of copper is $0.09cal/g/{}^{0}C,$ then $\left( {{L}_{f}}=80cal/gm \right)$
A. Mass of calorimeter is 0.5 kg
B. Thermal capacity of the calorimeter is $4.5ca{{l}^{0}}/C$
C. The heat required to raise the temperature of the calorimeter by ${{8}^{0}}C$ will be 36 cal.
D. Heat required to melt 15gm of ice at $0{}^\circ C$ placed in the calorimeter will be 1200 cal.

Answer 1

Hint: We have been provided with water equivalent value. Use the concept of water equivalent formula, which is a product of mass and specific heat. Also according to options, we have different requirements. Therefore use a formula of heat energy which will give a relation between temperature, mass and specific heat.

Formula used:
Water equivalent $=ms$
Where, m= mass of copper
s= specific heat of copper
Specific heat capacity is given as
$c=\dfrac{Q}{m\Delta T}$
Where,
c= specific heat of substance
Q= heat required
m= mass of substance
$\Delta T=$Change in temperature.

Complete step by step answer:
In this question, we have given water equivalent of a copper calorimeter which is 4.5 g denoted by ${{E}_{q}}$
$\therefore {{E}_{q}}=4.5g$
Also, we have given specific heat of copper which is $0.09cal/g/{}^\circ c$ denoted by c.
$\therefore c=0.09cal/g/{}^\circ c$ .
In this question, it is already mentioned that, question has multiple correct options.
First let, see option number (A)
Here, we need to find out the mass of the calorimeter =?
We know that, the product of mass of body and specific heat is equal to mass of water equivalent, numerically. This is known as the water equivalent.
Therefore, mathematically
m c = water equivalent $\left( {{E}_{q}} \right)$
Where,
m= mass of copper
We get,
$\begin{align}
  & \Rightarrow mc=4.5 \\
 & \Rightarrow m\left( 0.09 \right)=4.5 \\
 & \Rightarrow m\left( \dfrac{9}{100} \right)=\dfrac{45}{10} \\
 & \Rightarrow m=\dfrac{45\times 10}{9} \\
 & \Rightarrow m=50gm \\
 & \Rightarrow m=0.5kg \\
\end{align}$
Hence, the above answer is that the mass of copper $=0.5kg$ is not matching with the given answer, in option (A) because in option (A) mass of the calorimeter is given.
Therefore option (A) is not the correct answer.
Now taking about option (B):
To calculate thermal capacity which is also known as heat capacity, we have –
${{m}_{w}}\times {{c}_{w}}\times \Delta T={{m}_{c}}\times {{c}_{c}}\times \Delta T=Q$
$\Rightarrow $ Water equivalent $=g=ms=4.5cal/{}^\circ c$
Since, water equivalent $=\dfrac{ms}{sw}$
Where, s w = specific heat of water which is equal to $sw=1cal/{}^\circ c\left( \text{in 4}\text{.2 joule/k} \right)$
Therefore, option (B) is the correct option.
Now let’s consider option (C).
We know that the amount of heat required to change the temperature of a substance is directly proportional to the mass of the substance and change in the temperature $\Delta \text{T}$ which is given mathematically as,
$Q=cm\Delta T$
Where,
Q= heat required
$\Delta T=$ Change in temperature
C = specific heat
m = mass of body / substance.
Put value in $Q=cm\Delta T$
$\begin{align}
  & Q=4.5\times l\times 8 \\
 & Q=36cal \\
\end{align}$
Hence, the heat required to raise the temperature of the calorimeter by $8{}^\circ c$ is 36 cal. Option (C) is the correct option.
Let’s see option (D).
We know that specific heat of ice is$0.5cal/g/{}^\circ c$ .
Put value in $Q=cm\Delta T$
$\begin{align}
  & \Rightarrow Q=15\times 0.5\times 273k \\
 & \Rightarrow Q=2047.5cal \\
\end{align}$
Above value does not match with the given value.
Therefore, option (D) is an incorrect option.
Hence only option (B) and option (C) are correct options.

Note:
Conversion of calories into joule will lead to change your answer; in the first option we have provided the value of mass of the calorimeter by note that was the value of the mass of copper. Water equivalent comes under the physics properties of water. Equivalent weight of water and equivalent mass is nothing but actual physics bulk of a substance while weight is the gravitational force of mass. So the unit of water equivalent is kg.