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Molar and Specific Heat Capacity

A 140 W heate...

Question

A $140 W$ heater was placed in $2.00 k g$ of methanol $(C H_{3} O H)$ and turned on for exactly 2 min. The temperature increased by $4.24 K$ . Assuming that all the heat is absorbed by methanol, then molar heat capacity of methanol (in $J m o l^{- 1} K^{- 1}$ ) is (Report the answer to the closest integer)

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Solution

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

Mass of methanol $= 2.0 k g = 2000 g$
Rise in temperature ( $Δ T) = 4.24 K$
we know
$∵ q = m C_{s} Δ T$
where $C_{s}$ = specific heat capacity
$q$ = heat absorbed
$m$ = mass of substance
$Δ T$ = change in tempearture

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

$C_{s} = 1.98 J g^{- 1} K^{- 1}$
molar mass of methanol = $32 g / m o l$
$= 1.98 \times 32 J m o l^{- 1} K^{- 1}$
$= 63.4 \approx 63.0 J m o l^{- 1} K^{- 1}$

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