If 32 gm of \(O_2\)${\mathrm{}}_{}$ at \(27^{\circ}\mathrm{C}\) is mixed with 64 gm of \(O_2\)${\mathrm{}}_{}$ at \(327^{\circ}\mathrm{C}\) in an adiabatic vessel, then the final temperature of the mixture will be:
1. \(200^{\circ}\mathrm{C}\)
2. \(227^{\circ}\mathrm{C}\)
3. \(314.5^{\circ}\mathrm{C}\)
4. \(235.5^{\circ}\mathrm{C}\)$\mathrm{}$

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

Hot water cools from 60$°\mathrm{C}$ to 50$°\mathrm{C}$ in first 10 minutes and from 50$°\mathrm{C}$ to 42$°\mathrm{C}$ in next 10 minutes. The temperature of surrounding is :

1.  $5° \mathrm{C}$

2.  $10° \mathrm{C}$

3.  $15° \mathrm{C}$

4.  $20°\mathrm{C}$

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

1.  ${\alpha }_c > {\alpha }_f$

2.  ${\alpha }_f > {\alpha }_c$

3.  ${\alpha }_f = {\alpha }_c$

4.  ${\alpha }_f + {\alpha }_c = 0$

A pendulum clock runs faster by 5 seconds per day at \(20^{\circ}\mathrm {C}\) and goes slow by 10 second per day at \(35^{\circ}\mathrm {C}\). It shows the correct time at a temperature of:
1. \(27.5^{\circ}\mathrm {C}\)
2. \(25^{\circ}\mathrm {C}\)
3. \(30^{\circ}\mathrm {C}\)
4. \(33^{\circ}\mathrm {C}\)
 

The temperature of a body on Kelvin scale is found to be X K. When it is measured by a Fahrenheit thermometer, it is found to be X⁰F. Then X is

(1) 301.25

(2) 574.25

(3) 313

(4) 40

One kilogram of ice at $0°$C is mixed with one kilogram of water at 80$°C$. The final temperature of the mixture is (Take: Specific heat of water = 4200 J $k{g}^{-1}{C}^{-1}$, Latent heat of ice = 336 kJ $k{g}^{-1}$)

(1) $0°$C              (2) $50°C$

(3) $40°C$           (4) $60°C$

Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at ${100}^{°}$ C, while the other one is at $0^{° }$C. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is -

(1) ${50}^{°} C$

(2) more than ${50}^{°}$C

(3) less than ${50}^{°}$C but greater than $0^{°}$C

(4)  $0 {}_{0}C$