A constant volume gas thermometer shows pressure reading of $50 \,cm$ and $90 \,cm$ of mercury at $0^{\circ} C$ and $100^{\circ} C$ respectively. When the pressure reading is $60 \,cm$ of mercury, the temperature is ……… $^{\circ} C$

$50\, gm$ of copper is heated to increase its temperature by $10\,^oC$. If the same quantity of heat is given to $10\, gm$ of water, the rise in its temperature is …….. $^oC$ (Specific heat of copper $=420\, Joule\, kg^{-1}\,^oC^{-1}$)

A coffee maker makes coffee by passing steam through a mixture of coffee powder, milk and water. If the steam is mixed at the rate of $50 \,g$ per minute in a mug containing $500 \,g$ of mixture, then it takes about $t_0$ seconds to make coffee at $70^{\circ} C$ when the initial temperature of the mixture is $25^{\circ} C$. The value of $t_0$ is close to ………. $s$ (ratio of latent heat of evaporation to specific heat of water is $540^{\circ} C$ and specific heat of the mixture can be taken to be the same as that of water)

A pendulum clock keeps correct time at $0\,^oC$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha $. If the temperature rises to $t\,^oC$, then the clock loses per day by (in second)

A cylindrical rod with one end in a steam chamber and the outer end in ice results in melting of $0.1 \,\,gm$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $1/4$ that of first, the rate at which ice melts is $gm/sec$ will be