Question 842: Thermodynamics & KTG

Question

The volume of a metal block increases by $$0.225 \%$$ when its temperature is increased by $$30^{\circ} \mathrm{C}$$. Hence coefficient of linear expansion of the material of metal block is

Accepted Answer

The increase in volume is $$\frac{\Delta \mathrm{V}}{\mathrm{V}} 	imes 100=0.225$$
Change in temperature is $$\Delta \mathrm{T}=30^{\circ} \mathrm{C}$$
We know, $$\gamma=3 \alpha$$
$$	herefore \quad$$ The change in volume is $$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$$
$$\begin{aligned}
& 	herefore \quad \frac{\Delta V}{V} 	imes 100=3 \alpha \Delta \mathrm{T} 	imes 100 \
& 	herefore \quad 0.225=3 \alpha 	imes 30 	imes 100 \
& 	herefore \quad \alpha=\frac{0.225}{3 	imes 30 	imes 100} \
& 	herefore \quad \alpha=2.5 	imes 10^{-5} /{ }^{\circ} \mathrm{C}
\end{aligned}$$

Answer

$$7.5 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$$.

Answer

$$6.75 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$$.

Answer

$$2.5 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$$.

Answer

$$1.5 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$$.

Thermodynamics & KTG

The volume of a metal block increases by $0.225 \% when its temperature is increased by 30^{\circ} \mathrm{C}$. Hence coefficient of linear expansion of the material of metal block is

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