Certain amount of heat is given to 100 g og copper to increase its temperature by $21^{\circ} \mathr

Question

Certain amount of heat is given to 100 g og copper to increase its temperature by $21^{\circ} \mathrm{C}$. If the same amount of heat is given to 50 g of water, then the rise in its temperature is (Specific heat capacity of copper $=400 \mathrm{Jg}^{-1} \mathrm{~K}^{-1}$ and that for water $=4200 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ )\

Professor PC Thomas Classes · Answer

Here, mass of copper,\ $\mathrm{m}_{\mathrm{c}_{\mathrm{u}}}=100 \mathrm{~g}=100 	imes 10^{-3} \mathrm{~kg}$\ Specific heat capacity of copper\ $\mathrm{S}_{\mathrm{C}_{\mathrm{u}}}=400 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$\ Mass of water, $\mathrm{m}_{\mathrm{w}}=50 \mathrm{~g}=50 	imes 10^{-3} \mathrm{~kg}$\ Specific heat capacity of water, $\mathrm{S}_{\mathrm{w}}+=4200 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$\ The amount of heat required to increase the temperature of copper by $21^{\circ} \mathrm{C}$ is\ $\mathrm{Q}=\mathrm{m}_{\mathrm{c}_{\mathrm{u}}} \mathrm{s}_{\mathrm{Clu}} \Delta \mathrm{T}_{1}=100 	imes 10^{-3} 	imes 400 	imes 21$\ According to given problem $\mathrm{Q}=\mathrm{Q}_{1}$\ $100 	imes 10^{-3} 	imes 400 	imes 21=50 	imes 10^{-3} 	imes 4200 	imes \Delta \mathrm{T}$\ $\Delta \mathrm{T}_{1}=\frac{2 	imes 21 	imes 4}{42}=4^{\circ} \mathrm{C}$\