Question

The molar heat capacity of water at constant pressure P, is $75J{{K}^{-1}}mo{{l}^{-1}}$. When 1.0kJ of heat is supplied to 100 g of water which is free to expand, the increase in the temperature of water is:
a.) 1.2K
b.) 2.4K
c.) 4.8K
d.) 6.6K

Answer 1

It is quite certain that if we apply heat to any system, there is an increment in the temperature of that system. The amount of heat added so as to increase the temperature by 1 unit is molar heat capacity. There is a relationship between the heat supplied, molar heat capacity and the temperature change.

Complete step by step answer:
-Heat transfer is the process of exchange of heat from 1 system to another. It can be done by conduction, convection or radiation. Conduction basically occurs in solids, convection in liquids and radiation in vacuum.
-To be able to solve the question, we must know total heat capacity, molar heat capacity and specific heat capacity of a substance.
Heat capacity is the heat needed to raise the temperature of a system by ${{1}^{\circ }}C$ under a given process. It is represented mathematically as ${{C}_{T}}=\dfrac{dq}{dT}J{{/}^{\circ }}C$ .
Molar heat capacity is the heat required to raise the temperature of 1 mole of a substance by unit degree. It is represented as $C=\dfrac{dq}{ndT}J/mol/K$

Specific heat capacity is the heat required to raise the temperature of a unit mass of a substance by unit degree temperature. It is represented mathematically as $s=\dfrac{dq}{mdT}J/g/K$ .
-In the question, we are given molar heat capacity. So for that we need to calculate the moles of water and then put it in the equation of heat which can be obtained by integrating the unit heat formula.

-We have seen that for molar heat capacity, mathematical representation is
$\begin{aligned} & C=\dfrac{dq}{ndT} \\\ & \Rightarrow \text{dq=nCdT} \\\ & \\\ \end{aligned}$
On integrating the above equation we get
$q=\int{nCdT=nC\Delta T}$

-Given the question, the weight of water is 100g. So the no. of moles of water will be
$\begin{aligned} & moles=\dfrac{wt.\text{ in g}}{molecular\text{ wt}} \\\ & \text{ = }\dfrac{100}{18}=5.55 \\\ \end{aligned}$

-Now using the formula of heat, we get
1000 = 5.55 x 75 x $\Delta T$
Thus, we get $\Delta T$ = 2.4K.
So, the correct answer is “Option B”.

Note: Always take care of the units while solving such numericals. Convert all the quantities in the same unit and decide the unit by seeing the unit of heat capacity. If heat capacity is given in J/K/mol, then convert the heat in joules and temperature in kelvin. If heat capacity is given in cal/K/mol then convert the heat in calories.