$A$ 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 $= 9000\,kg/m^3$)

$10 \, g$ of ice at $0^{\circ} C$ is kept in a calorimeter of water equivalent $10 \, g$. How much heat (in $cal$) should be supplied to the apparatus to evaporate the water thus formed? (Neglect loss of heat)

$A$ $10.0 \,W$ electrical heater is used to heat a container filled with $0.5 \,kg$ of water. It is found that the temperature of the water and the container rose by $3 \,K$ in $15 \,min$. The container is then emptied,dried,and filled with $2 \,kg$ of an oil. It is now observed that the same heater raises the temperature of the container-oil system by $2 \,K$ in $20 \,min$. Assuming no other heat losses in any of the processes,the specific heat capacity of the oil is ................ $\times 10^3 \,J K^{-1} kg^{-1}$.

Consider two thermometers $T_1$ and $T_2$ of equal length,which can be used to measure temperature over the range $\theta_1$ to $\theta_2$. $T_1$ contains mercury as the thermometric liquid,while $T_2$ contains bromine. The volumes of the two liquids are the same at the temperature $\theta_1$. The volumetric coefficients of expansion of mercury and bromine are $18 \times 10^{-5} \, K^{-1}$ and $108 \times 10^{-5} \, K^{-1}$,respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are $d_1$ and $d_2$,respectively,then the ratio $d_1: d_2$ is closest to:

$A$ geyser heats water flowing at the rate of $3.0 \, L/min$ from $27 \, ^{\circ}C$ to $77 \, ^{\circ}C$. If the geyser operates on a gas burner,what is the rate of consumption (in $g/min$) of the fuel if its heat of combustion is $4.0 \times 10^{4} \, J/g$?

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?