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Question

Some helium occupies 1200 ft31200 \mathrm{~ft}^3 at 70°F70{\degree} \mathrm{F}. Find the temperature at which its volume will be 600 ft3600 \mathrm{~ft}^3.

Solution

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Answered 2 years ago
Answered 2 years ago
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Given:\textbf{Given:}

V1=1200 ft3V_1=1200 \text{ ft}^3

V2=600 ft3V_2=600 \text{ ft}^3

T1=70 F=530RT_1=70 ^\circ \text{ F}=530 ^\circ \text{R}

To solve the problem we use Charles's law which reads:

V1T1=V2T2\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}

From it we express T2T_2 and by entering the data given in the task we get the result:

T2=V2T1V1=6005301200T2=265R\begin{align*} T_2&=\dfrac{V_2 \cdot T_1}{V_1}\\ &=\dfrac{600 \cdot 530}{1200}\\ &\boxed{T_2=265^\circ \text{R} } \end{align*}

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