If the $emf$ of a thermocouple,one junction of which is kept at $0\,^{\circ}C$,is given by $e = at + 1/2\,bt^2$,then the neutral temperature will be

How much thermal energy is required to change a $40 \ g$ ice cube from solid at $-10^{\circ} C$ to steam at $110^{\circ} C$ (in $kcal$)?
[Assume, latent heat of fusion for water $= 80 \ kcal/kg$, specific heat of water $= 1 \ kcal/kg^{\circ} C$, specific heat of ice $= 0.5 \ kcal/kg^{\circ} C$, specific heat of steam $= 0.48 \ kcal/kg^{\circ} C$, latent heat of vaporisation of water $= 540 \ kcal/kg$]

$A$ refrigerator converts $500\,g$ of water at $25\,^{\circ}C$ into ice at $-10\,^{\circ}C$ in $3\,hours\,40\,minutes$. The quantity of heat removed per minute is ........ $cal/\min$.
(Specific heat of water $= 1\,cal/g\,^{\circ}C$,Specific heat of ice $= 0.5\,cal/g\,^{\circ}C$,Latent heat of fusion $= 80\,cal/g$)

In the given triple point curve as shown in the figure,the curves $AO$,$BO$,and $CO$ represent:

Give one example each for solid,liquid,and gas showing expansion with an increase in temperature and contraction with a decrease in temperature.

$A$ copper ring has a diameter of exactly $25 \, mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05 \, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and the two are allowed to come to thermal equilibrium,with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere to the ring is: (Given: $\alpha_{Cu} = 17 \times 10^{-6} /^o C$,$\alpha_{Al} = 2.3 \times 10^{-5} /^o C$,specific heat of $Cu = 0.0923 \, cal/g^o C$,and specific heat of $Al = 0.215 \, cal/g^o C$)