When $1\, g$ of water at $0^{\circ}C$ and $1 \times 10^5\, N/m^2$ pressure is converted into ice of volume $1.091\, cm^3$,the external work done will be (in $, J$)

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 $\alpha$.

$A$ thermally insulated vessel contains some water at $0^{\circ}C$. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given that the latent heat of vaporization of water at $0^{\circ}C = 21 \times 10^5 \text{ J/kg}$ and the latent heat of fusion of water $= 3.36 \times 10^5 \text{ J/kg}$. The maximum percentage amount of water that will be solidified in this manner will be ...... $\%$

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 $; J$)

Liquid oxygen at $50 \, K$ is heated to $300 \, K$ at a constant pressure of $1 \, atm$. If the rate of heating is constant,which of the following graphs represents the variation of temperature with time?

$A$ glass flask of volume $1$ litre is fully filled with mercury at $0\,^{\circ}C$. Both the flask and mercury are now heated to $100\,^{\circ}C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^{\circ}C$ and the coefficient of linear expansion of glass is $10 \times 10^{-6}/^{\circ}C$,the amount of mercury which is spilled out is ............ $ml$. (in $.2$)