The volume of a gas at 20^{circ}C is 100 , cm | vedclass

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Question

(D) The relationship between volume and temperature at constant pressure is given by $V_t = V_0(1 + \gamma t)$,where $\gamma$ is the volume expansion

Vedclass · Accepted Answer

$0.0033 \, ^{\circ}C^{-1}$

Vedclass · Answer

(D) The relationship between volume and temperature at constant pressure is given by $V_t = V_0(1 + \gamma t)$,where $\gamma$ is the volume expansion coefficient.For two different temperatures $t_1$ and $t_2$,we have $\frac{V_1}{V_2} = \frac{1 + \gamma t_1}{1 + \gamma t_2}$.Given $V_1 = 100 \, cm^3$ at $t_1 = 20^{\circ}C$ and $V_2 = 125 \, cm^3$ at $t_2 = 100^{\circ}C$.Substituting the values: $\frac{100}{125} = \frac{1 + 20\gamma}{1 + 100\gamma}$.Simplifying the fraction: $0.8 = \frac{1 + 20\gamma}{1 + 100\gamma}$.$0.8(1 + 100\gamma) = 1 + 20\gamma$.$0.8 + 80\gamma = 1 + 20\gamma$.$60\gamma = 0.2$.$\gamma = \frac{0.2}{60} = \frac{1}{300} \approx 0.0033 \, ^{\circ}C^{-1}$.

The volume of a gas at $20^{\circ}C$ is $100 \, cm^3$ at normal pressure. If it is heated to $100^{\circ}C$,its volume becomes $125 \, cm^3$ at the same pressure,then the volume coefficient of the gas at normal pressure is:

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