If $\lambda_m$ is the wavelength, corresponding to which the radiant intensity of a block is at its maximum and its absolute temperature is $T,$ then which of the following graphs correctly represents the variation of $T?$

1.		2.
3.		4.

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.  $20°\mathrm{C}$

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. $33^{\circ}\mathrm {C}$

A constrained steel rod of length $l$, area of cross-section $A$, Young's modulus $Y$ and coefficient of linear expansion $\alpha$ is heated through $t^{\circ}\text{C}$. The work that can be performed by the rod when heated is:
1. $(YA\alpha t)(l\alpha t)$
2. $\frac{1}{2}(YA\alpha t)(l\alpha t)$
3. $\frac{1}{2}(YA\alpha t)\frac{1}{2}(l\alpha t)$
4. $2(YA\alpha t)(l\alpha t)$

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

A temperature of $100^{\circ}\text {F}$ (Fahrenheit scale) is equal to $T~\text{K}$ (Kelvin scale). The value of $T$ is:
1. $310.9$
2. $37.8$
3. $100$
4. $122.4$