A pendulum clock runs faster by \(5\) s per day at \(20^{\circ}\mathrm {C}\) and goes slow by \(10\) s 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

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

1.  ${\alpha }_c > {\alpha }_f$

2.  ${\alpha }_f > {\alpha }_c$

3.  ${\alpha }_f = {\alpha }_c$

4.  ${\alpha }_f + {\alpha }_c = 0$

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.  $20°\mathrm{C}$

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

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

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. \(235.5^{\circ}\mathrm{C}\)$\mathrm{}$

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)  $0 {}_{0}C$

A body cools from a temperature 3T to 2T in10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be:
1. \(\frac{7}{4}T\)
2. \(\frac{3}{2}T\)
3. \(\frac{4}{3}T\)
4. \(T\)