Calorimetry And Heat Capacity

NCERT Class 11, Chapter 11 (Thermal Properties of Matter) defines the heat required to change a substance's temperature as $Q=mc\Delta T$, where $m$ is mass, $c$ the specific heat capacity, and $\Delta T$ the temperature change. Specific heat measures how much energy one kilogram of a substance needs to warm by one degree. Here $\Delta T=75-25=50{}^{\circ }\text{C}$. Substituting $m=0.5\text{kg}$, $c=4200{\text{J/kg}}^{\circ }\text{C}$ and $\Delta T=50$ gives $Q=0.5\times 4200\times 50=105000\text{J}$. The option 52500 J halves the temperature rise wrongly. The option 210000 J ignores the half-kilogram mass. The option 21000 J uses a 10°C rise instead of 50°C. As a magnitude check, water's high specific heat means even modest heating demands a large amount of energy, which is why water is an effective coolant, confirming that 105 kJ for this process is reasonable in both value and joule units.