Air (sp. Heat at room temperature and 1 atm=0.71 J/g K ; density) $\left.=1.22\times {10}^{-6} \mathrm{kg}{ \mathrm{cm}}^3\right)$ present in a room (dimensions $6\times 5\times 4{\mathrm{m}}^3$ ) got heated up when a bulb of 500 watt was switched on for 10 minutes, the increase in room temperature if heat capacity of four walls and roof is $60\times {10}^3\mathrm{J}/\mathrm{K}$ is:

1 Watt=1 J/s ; volume of room $=6\times 5\times 4{\mathrm{m}}^3=120{ \mathrm{m}}^3=120\times {10}^6{ \mathrm{cm}}^3$; 

Wt. of air in room= volume x density$=120\times {10}^6{ \mathrm{cm}}^3\times 1.22\times {10}^{-6} \mathrm{kg}{ \mathrm{cm}}^{-3}$

$=120\times {10}^6\times 1.22\times {10}^{-6}\times {10}^3\mathrm{g}=146400\mathrm{g}$

Heat given out by bulb=500 watt x (10 x 60) s

                                                =500 J/s x 600s

$=3\times {10}^5\mathrm{J} [\because 1\text{ watt }=1\mathrm{J}/\mathrm{s}]\mathrm{s}$

$\text{ Heat gained by (walls+roof) }=60\times {10}^3 \mathrm{J}/\mathrm{K}\left(\mathrm{\Delta T}\right)$

$\text{ Heat gained by air }=0.71{\mathrm{Jg}}^{-}{\mathrm{K}}^{-}\times 146400 \mathrm{g}\times \Delta T$

But heat given out by bulb= Heat gained by (walls+roof)+Heat gained by air

$$\begin{gathered} 3\times {10}^5\mathrm{J}=60\times {10}^3{\mathrm{JK}}^{-}\left(\mathrm{\Delta T}\right)+0.71\times 146400{\mathrm{JK}}^{-}\times \mathrm{\Delta T} \\ 3\times {10}^5\mathrm{J}=\mathrm{\Delta T}\left[60\times {10}^3+0.71\times 146400\right]{\mathrm{JK}}^{-}=163944{\mathrm{JK}}^{-}\times \mathrm{\Delta T} \\ \mathrm{\Delta T}=\frac{3\times {10}^5\mathrm{J}}{163944\mathrm{JK}}=1.83\mathrm{K} \end{gathered}$$