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\(=336~\text{kJ kg}^{-1}\))

$80 \mathrm{g} \mathrm{of} \mathrm{water} \mathrm{at} 30°\mathrm{C} \mathrm{is} \mathrm{poured} \mathrm{on} \mathrm{a} \mathrm{large} block$
$\mathrm{of} \mathrm{ice} \mathrm{at} 0°\mathrm{C}. \mathrm{The} \mathrm{mass} \mathrm{of} \mathrm{ice} \mathrm{that} \mathrm{melts} \mathrm{is}$

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

$\mathrm{If} {\mathrm{\alpha }}_{\mathrm{c}} \mathrm{and} {\mathrm{\alpha }}_{\mathrm{f}} \mathrm{denote} \mathrm{the} \mathrm{numerical} \mathrm{values} \mathrm{of} \mathrm{coefficient} \mathrm{of} \mathrm{linear}$
$\mathrm{expansion} \mathrm{of} \mathrm{a} \mathrm{solid}, \mathrm{expressed} \mathrm{per} °\mathrm{C} \mathrm{and} \mathrm{per} °\mathrm{F} \mathrm{respectively},$
$\mathrm{then}$

1.  ${\alpha }_c > {\alpha }_f$

2.  ${\alpha }_f > {\alpha }_c$

3.  ${\alpha }_f = {\alpha }_c$

4.  ${\alpha }_f + {\alpha }_c = 0$

$$\begin{gathered} \mathrm{A} \mathrm{pendulum} \mathrm{clock} \mathrm{runs} \mathrm{fast} \mathrm{by} 5 \sec . \mathrm{per} \mathrm{day} \mathrm{at} 20°\mathrm{C} \mathrm{and} \mathrm{goes} \mathrm{slow} \\ \mathrm{by} 10 \sec . \mathrm{per} \mathrm{day} \mathrm{at} 35°\mathrm{C}. \mathrm{It} \mathrm{shows} \mathrm{correct} \mathrm{time} \mathrm{at} \mathrm{a} \mathrm{temperature} \mathrm{of} \end{gathered}$$

1.  $27.5°\mathrm{C}$

2.  $25°\mathrm{C}$

3.  $30°\mathrm{C}$

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: