Question

$100\text{ g}$ water is heated from $30{}^\circ \text{ C}$ to$50{}^\circ \text{ C}$ . Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184$\text{J/kg K}$ )
(A) $4\cdot 2\text{ K J}$
(B) $8\cdot 4\text{ K J}$
(C) $\text{84 K J}$
(D) $2\cdot 1\text{ K J}$

Answer 1

Hint The formula for internal energy (or heat) is equal to:
$\text{Q}=\text{mc}\vartriangle \text{T}$
By substituting the given values in the above equation, the answer can be formed

Complete step by step solution
We know that,
$\begin{aligned} & \text{c}=4184\text{ j/kg K} \\\ & \text{m}=100\text{ gm} \\\ & \text{ }=0\cdot 1\text{ kg} \\\ \end{aligned}$
$\begin{aligned} & \vartriangle \text{T}=50{}^\circ \text{ C}-30{}^\circ \text{ C} \\\ & \text{ }=20{}^\circ \text{ C} \\\ & \text{ }=323\cdot 15\text{ K}-303\cdot 15\text{ K} \\\ & \text{ }=20\text{ K} \\\ & \text{ }\left[ {}^\circ \text{C}+273\cdot 15=\text{K} \right] \\\ \end{aligned}$
We know that change in internal energy is equal to heat dissipated and is given by:
$\text{Q}=\text{mc}\vartriangle \text{T}$
Substituting the above values in this equation, we get
$\begin{aligned} & \text{Q}=0\cdot 1\times 4184\times 20 \\\ & \text{ }=8368\text{ J} \\\ \end{aligned}$
$\begin{aligned} & \text{Q}=8\cdot 368\text{ K J} \\\ & \text{ }=8\cdot 4\text{ K J} \\\ \end{aligned}$

So correct option is (B)

Note The heat capacity measures the amount of heat which is important to raise the temperature of an object or system by one degree calcium. It is denoted by C.
$\text{C}=\frac{\text{Q}}{\text{m}\vartriangle \text{T}}$
Or $\text{Q}=\text{mc}\vartriangle \text{T}$
Heat capacity is an extensive property. It depends upon the temperature, pressure and volume of the system under consideration.
The heat transferred Q causes a temperature $\vartriangle \text{T}$. The amount of heat transfer also depends upon mass.