One kilogram of ice at \(0^\circ \text{C}\) is mixed with one kilogram of water at \(80^\circ \text{C}.\) The final temperature of the mixture will be: (Take: Specific heat of water = \(4200~\text{J kg}^{-1}\text{K}^{-1},\) latent heat of ice\(=336~\text{kJ kg}^{-1}\))

1.	\(0^\circ \text{C}\)	2.	\(50^\circ \text{C}\)
3.	\(40^\circ \text{C}\)	4.	\(60^\circ \text{C}\)

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$<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{ice}<mspace\; width="1em"></mspace>\mathrm{at}<mspace\; width="1em"></mspace>0°\mathrm{C}.<mspace\; width="1em"></mspace>\mathrm{The}<mspace\; width="1em"></mspace>\mathrm{mass}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{ice}<mspace\; width="1em"></mspace>\mathrm{that}<mspace\; width="1em"></mspace>\mathrm{melts}<mspace\; width="1em"></mspace>\mathrm{is}<mspace\; width="1em"></mspace>$

1.  15 g

2.  30 g

3.  50 g

4  60 g

A black body at temperature 300K radiates heat at the rate E. If its temperature is increased by 600K, the rate of radiation will increase to -

1.  16E

2.  64E

3.  81E

4.  256E

Heat capacity is equal to the product of:

1.  mass and gas constant

2.  mass and specific heat

3.  latent heat and volume of water

4.  mass and Avogadro number

When a block of iron floats in Hg at $0°C$, a fraction $K_1$ of its volumen= is submerged, while at temperature of $60°C$ a fraction $K_2$ is seen to be submersed. If the coefficient of volume expansion of iron is ${\gamma }_{Fe}$ and that of mercury is ${\gamma }_{Hg}$, then the ratio $\frac{K_1}{K_2}$ can be expressed as:

(1) $\frac{1+60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$

(2) $\frac{1-60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$

(3) $\frac{1+60{\gamma }_{Fe}}{1-60{\gamma }_{Hg}}$

(4) $\frac{1+60{\gamma }_{He}}{1-60{\gamma }_{Fe}}$

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$<mspace\; width="1em"></mspace>\mathrm{then}$

1.  ${\alpha }_c<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\alpha }_f<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.  ${\alpha }_f<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\alpha }_c<mspace\; width="1em"></mspace>$

3.  ${\alpha }_f<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\alpha }_c<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

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1.  $27.5°\mathrm{C}<mspace\; width="1em"></mspace>$

2.  $25°\mathrm{C}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $30°\mathrm{C}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.  $33°\mathrm{C}$

Two identical bodies are made of a material whose heat capacity increases with temperature. One of these is at ${\mathrm{}}^{}$\(100^{\circ} \mathrm{C}\), while the other one is at ${\mathrm{}}^{}$\(0^{\circ} \mathrm{C}\). If the two bodies are brought into contact, then assuming no heat loss, the final common temperature will be:

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4x10⁵J/Kg and g=10N/Kg]

1. 544 km

2. 136 km

3.  68  km

4.  34 km

The value of the coefficient of volume expansion of glycerin is \(5\times10^{-4}\) K^-1. The fractional change in the density of glycerin for a temperature increase of \(40^\circ \mathrm{C}\) will be: