Hot water cools from $60^{\circ} C$ to $50^{\circ} C$ in the first $10 \ min$ and to $42^{\circ} C$ in the next $10 \ min$. Then the temperature of the surroundings is (in $^{\circ} C$)

Assuming Newton's law of cooling to be valid,a body at temperature $50^{\circ} C$ in a surrounding of temperature $20^{\circ} C$ achieves a steady state with the help of a $100 \ W$ heater. If the same body has a temperature of $35^{\circ} C$ in the same surrounding,then the power of the heater required to maintain a steady state is ........ $W$.

According to Newton's law of cooling,the rate of cooling of a body is directly proportional to the ........

If a liquid cools from $95^{\circ}C$ to $90^{\circ}C$ in $30 \, s$ and from $55^{\circ}C$ to $50^{\circ}C$ in $70 \, s$,then the temperature of the surroundings is ...... $^{\circ}C$. (in $.5$)

$A$ cubic metal block of mass $5 \,kg$ and edge length $0.1 \,m$ at an initial temperature of $100^{\circ} C$ is placed on a thermally insulating flat surface and exposed to air at $0^{\circ} C$. The time in seconds required to cool the block to a temperature of $37^{\circ} C$ is closest to. (Note: Specific heat of the metal $= 500 \,J/kg/^{\circ}C$; Heat transfer coefficient from block to air $= 50 \,W/m^2/^{\circ}C$)

$A$ sphere,a cube,and a thin circular plate,all of the same material and same mass,are initially heated to the same high temperature and allowed to cool down under similar conditions. Then,the