NCERT Solutions for Chapter: Thermal Properties of Matter, Exercise 5: LA

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say $10 \mathrm{cm}.$We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If ${\alpha }_{iron}=1.2\times {10}^{-5}/K$ and ${\alpha }_{brass}=1.8\times {10}^{-5}/K$, what should we take as length of each strip?

We would like to make a vessel whose volume does not change with temperature. We can use brass and iron (${\gamma }_{brass}=6\times {10}^{-5}{K}^{-1}$ and ${\gamma }_{iron}=3.55\times {10}^{-5}{K}^{-1}$) to create a volume of $100\mathrm{cc}.$ How do you think you can achieve this?

 Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57°\mathrm{C}$ is drunk. You can take body (tooth) temperature to be $37°$C and $\alpha =1.7\times {10}^{-5}/\mathrm{K}.$ Bulk modulus for copper $=140\times {10}^9\mathrm{N}/{\mathrm{m}}^2$.

A rail track made of steel having length $10 \mathrm{m}$  is clamped on a railway line at its two ends.

On a summer day due to rise in temperature by $20°\mathrm{C}$, it is deformed as shown in the figure above. Find $x$ (displacement of the centre) if ${\alpha }_{steel}=1.2\times {10}^{-5}{/}^{\mathrm{o}}\mathrm{C}$.

 A thin rod having length $L_0$ at $0^{o}C$ and coefficient of linear expansion $\alpha$ has its two ends maintained at temperatures ${\theta }_1$ and ${\theta }_2$, respectively. Find its new length.

According to Stefan's law of radiation, a black body radiates energy $\sigma T^4$ from its unit surface area every second where $T$ is the surface temperature of the black body and $\sigma =5.67\times {10}^{-8} \mathrm{W}/{\mathrm{m}}^2/{\mathrm{K}}^4$ is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius $0.5 \mathrm{m}$. When detonated, it reaches temperature of ${10}^6 \mathrm{K}$ and can be treated as a black body. Estimate the power it radiates.

According to Stefan's law of radiation, a black body radiates energy $\sigma T^4$ from its unit surface area every second where $T$ is the surface temperature of the black body and $\sigma =5.67\times {10}^{-8}\mathrm{W}/{\mathrm{m}}^2/{\mathrm{K}}^4$ is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius $0.5 \mathrm{m}$. When detonated, it reaches temperature of ${10}^6 \mathrm{K}$ and can be treated as a black body. If surrounding has water at $30°\mathrm{C}$, how much water can $10\%$ of the energy produced evaporate in $1 \mathrm{s}$?

(${\mathrm{S}}_{\mathrm{W}}=4186.0 \mathrm{J}/\mathrm{kg}/K$, $L_{\mathrm{V}}=22.6\times {10}^5 \mathrm{J}/\mathrm{kg}$) (Given: Power radiated$=1.8\times {10}^{17}$ Watt)

According to Stefan's law of radiation, a black body radiates energy $\sigma T^4$ from its unit surface area every second where $T$ is the surface temperature of the black body and $\sigma =5.67\times {10}^{-8}\mathrm{W}/{\mathrm{m}}^2/{\mathrm{K}}^4$is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius $0.5 \mathrm{m}$. When detonated, it reaches temperature of ${10}^6 \mathrm{K}$ and can be treated as a black body.  If all this energy $U$ is in the form of radiation, corresponding momentum is $P=\frac{U}{c}.$How much momentum per unit time does it impart on unit area at a distance of $1 \mathrm{km}?$ [Power radiated $=1.8\times {10}^{17}$ Watt ]