Question

The molar heat capacity $\left( {{C_p}} \right)$ of water at constant pressure is $75J{K^{ - 1}}mo{l^{ - 1}}$ . The increase in temperature (in $K$) of $100g$ of water when $1kJ$ of heat is supplied to it is:
a.) $2.4$
b.) $0.24$
c.) $1.3$
d.) $0.13$

Answer 1

Hint: This question gives the knowledge about the molar heat capacity at constant pressure. Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. It is generally represented as ${C_p}$ .

Formula used: The formula used to determine the molar heat capacity at constant pressure is as follows:
${C_p} = \dfrac{{{q_p}}}{{n.\Delta T}}$
Where, ${C_p}$ is the molar heat capacity at constant pressure, ${q_p}$ is the absorbed heat at constant pressure, $n$ is the number of moles and $\Delta T$ is the change in temperature.
The formula to determine the number of moles is as follows:
$n = \dfrac{m}{M}$
Where, $m$ is the given weight, $n$ is the number of moles and $M$ is the molecular weight.

Complete step by step answer:
Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. Molar heat capacity at constant pressure is generally represented as ${C_p}$ .
- Now, we will determine the change in temperature using the formula of molar heat capacity.
The formula used to determine the molar heat capacity at constant pressure is as follows:
$ \Rightarrow {C_p} = \dfrac{{{q_p}}}{{n.\Delta T}}$
Rearrange the above formula to determine the change in temperature as follows:
$ \Rightarrow \Delta T = \dfrac{{{q_p}}}{{n.{C_p}}}$
- Here, we require the number of moles as well. So, first we will determine the number of moles of water.
The formula to determine the number of moles is as follows:
$ \Rightarrow n = \dfrac{m}{M}$
The molecular weight of water is $18gmo{l^{ - 1}}$ and the given weight of water is $100g$. Substitute these values in the above formula as follows:
$ \Rightarrow n = \dfrac{{100}}{{18}}$
On simplifying, we get
$ \Rightarrow n = 5.55$
- Now substitute $n$ as $5.55mol$ , ${q_p}$ as $1000J$ and ${C_p}$ as $75J{K^{ - 1}}mo{l^{ - 1}}$ in the formula to determine temperature change.
$ \Rightarrow \Delta T = \dfrac{{1000}}{{5.55 \times 75}}$
On simplifying, we get
$ \Rightarrow \Delta T = 2.4$
Therefore, the change in temperature is $2.4K$.
The correct option is option “A” .

Note: Always remember the concept that molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. And specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.