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(C) According to the ideal gas law for one mole of gas,$PV = RT$.Since pressure $P$ is constant,$V = (R/P)T$,which implies $V \propto T$.Let the initi

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$\frac{1}{T}$

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(C) According to the ideal gas law for one mole of gas,$PV = RT$.Since pressure $P$ is constant,$V = (R/P)T$,which implies $V \propto T$.Let the initial volume be $V_1$ at temperature $T_1 = T$.If the temperature increases by $1 \ K$,the new temperature is $T_2 = T + 1$.The new volume $V_2$ is given by $V_2 = (R/P)(T + 1)$.The increase in volume is $\Delta V = V_2 - V_1 = (R/P)(T + 1) - (R/P)T = R/P$.The ratio of the increase in volume to the original volume is $\frac{\Delta V}{V_1} = \frac{R/P}{(R/P)T} = \frac{1}{T}$.

At constant pressure,the ratio of the increase in volume of an ideal gas per degree rise in Kelvin temperature to its original volume is $(T =$ absolute temperature of the gas$)$

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