Question
The molar heat capacity $$C$$ of water at constant pressure is $$75\,J{K^{ - 1}}\,mo{l^{ - 1}},$$ 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.
4.8$$\,K$$
B.
6.6$$\,K$$
C.
1.2$$\,K$$
D.
2.4$$\,K$$
Answer :
2.4$$\,K$$
Solution :
$$\eqalign{
& {\text{According to heat capacity rule,}} \cr
& q = mc\Delta T,\,\,c = \frac{q}{{m\left( {{T_2} - {T_1}} \right)}} \cr
& {\text{Given that,}}\,\,c = 75\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& q = 1.0\,kJ = 1000J \cr
& {\text{Mass}} = 100\,g\,{\text{water}} \cr
& {\text{Molar mass of water}} = 18g \cr} $$
$$75 = \frac{{1000}}{{5.55 \times \Delta T}}$$ $$\left( {{\text{number of moles}} = \frac{{100}}{{18}} = 5.55} \right)$$
$$\eqalign{
& \therefore \,\,\Delta T = \frac{{1000}}{{5.55 \times 75}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2.4\,K \cr} $$