2003 AIPMT ThermodynamicsHeat Capacity Easy Question 72 of 82 in Thermodynamics

The molar heat capacity of water at constant pressure, C, is 75 J K$^{-1}$ 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 1.2 K
B 2.4 K
C 4.8 K
D 6.6 K

The answer is B.

Solution

Water is free to expand, so the heating is at constant pressure: $q = nC_p\Delta T$.
Number of moles of water: $n = \dfrac{100}{18} = 5.55$ mol
$q = 1.0$ kJ $= 1000$ J
$\Delta T = \dfrac{q}{nC_p} = \dfrac{1000}{5.55 \times 75} = \dfrac{1000}{416.7}$
$\Delta T = 2.4$ K

Concept Temperature rise from molar heat capacity

Thermodynamics in past papers

82 questions from this chapter have appeared across 26 exam years.