Question

The molar heat capacity of water at constant pressure is $84\, JK ^{-1} mol ^{-1}$. When $1.0\, kJ$ of heat is supplied to $100\, g$ of water which is free to expand; the increase in temperature of water is

• A. $3.8\, K$
• B. $2.1\, K$
• C. $4.8\, K$
• D. $1.5\, K$

Answer 1

Answer: (B)

Molar heat capacity of water per gram $=84 / 18=4.7\, J$
As we know that; $q=1\, kJ =1000\, J$
molar heat capacity $(q)=m \times c \times \Delta T$
where $m=$ mass, $c=$ specific heat capacity
$\Delta T=$ temperature change
$\therefore q=100 \times 4.7 \times \Delta T$
or $1000=100 \times 4.7 \times \Delta T$
$\Delta T=\frac{1000}{100 \times 4.7}=2.1\, K$
Thus, the increase in temperature of water is $2.1\, K$.