Question

A $140W$ heater was placed in $2.00kg$ of methanol $\left(C{H}_{3}OH\right)$ and turned on for exactly 2 min. The temperature increased by $4.24K$. Assuming that all the heat is absorbed by methanol, then molar heat capacity of methanol is

• A. $81.4Jmo{l}^{-1}{K}^{-1}$
• B. $36.50Jmo{l}^{-1}{K}^{-1}$
• C. $9.0Jmo{l}^{-1}{K}^{-1}$
• D. $63.4Jmo{l}^{-1}{K}^{-1}$

Answer 1

The correct option is D $63.4Jmo{l}^{-1}{K}^{-1}$

The power of the heater is
$140W=140J{s}^{-1}$
so, heat supplied in 2 min $=140J{s}^{-1}\times (60\times 2)s$
$q=16800J$

Mass of methanol $=2.0kg=2000g$
Rise in temperature ($\Delta T)=4.24K$
we know
$\because q=m{C}_s\Delta T$
where $C_s$ = specific heat capacity
$q$ = heat absorbed
$m$ = mass of substance
$\Delta T$ = change in tempearture

$\therefore$ Specific heat $=\frac{q}{m\Delta T}$
putting the values we get
$=\frac{16800J}{2000g\times 4.24K}$

$C_s=1.98J{g}^{-1}{K}^{-1}$
molar mass of methanol = $32g/mol$
$=1.98\times 32Jmo{l}^{-1}{K}^{-1}$
$=63.4Jmo{l}^{-1}{K}^{-1}$