Find the quantity of heat required to convert $40 \; g$ of ice at $-20^{\circ} C$ into water at $20^{\circ} C$. Given $L_{\text{ice}} = 0.336 \times 10^6 \; J/kg$,specific heat of ice $= 2100 \; J/kg \cdot K$,and specific heat of water $= 4200 \; J/kg \cdot K$. (in $; J$)

$A$ geyser heats water flowing at a rate of $2.0 \; kg$ per minute from $30^{\circ} C$ to $70^{\circ} C$. If the geyser operates on a gas burner,the rate of combustion of fuel will be $\dots \; g \min^{-1}$.
[Heat of combustion $= 8 \times 10^{3} \; J \cdot g^{-1}$,Specific heat of water $= 4.2 \; J \cdot g^{-1} \cdot {}^{\circ} C^{-1}$]

$A$ cylinder of mass $1\,kg$ is given heat of $20000\,J$ at atmospheric pressure. If the initial temperature of the cylinder is $20\,^oC$,then the work done by the cylinder will be .......$J$. (Given: Specific heat of cylinder $= 400\,J\,kg^{-1}\,^oC^{-1}$,Coefficient of volume expansion $= 9 \times 10^{-5}\,^oC^{-1}$,Atmospheric pressure $= 10^5\,N/m^2$,and density of cylinder $= 9000\,kg/m^3$)

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?

The figure shows a glass tube (linear coefficient of expansion is $\alpha$) completely filled with a liquid of volume expansion coefficient $\gamma$. On heating,the length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$.

During summers in India,one of the common practices to keep cool is to make ice balls of crushed ice,dip them in flavoured sugar syrup,and sip them. For this,a stick is inserted into crushed ice,and it is squeezed in the palm to make it into a ball. Equivalently in winter,in those areas where it snows,people make snowballs and throw them around. Explain the formation of a ball out of crushed ice or snow in the light of the $p-T$ diagram of water.