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(A) For a constant volume gas thermometer,the temperature $T$ is related to the pressure $P$ by the linear equation: $T = aP + b$.Given:At $T_0 = 0^{\

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$25$

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(A) For a constant volume gas thermometer,the temperature $T$ is related to the pressure $P$ by the linear equation: $T = aP + b$.Given:At $T_0 = 0^{\circ} C$,$P_0 = 50 \, cm$ of Hg.At $T_1 = 100^{\circ} C$,$P_1 = 90 \, cm$ of Hg.The slope of the temperature-pressure graph is $m = \frac{T_1 - T_0}{P_1 - P_0} = \frac{100 - 0}{90 - 50} = \frac{100}{40} = 2.5 \, ^{\circ} C/cm$.The equation for temperature is $T - T_0 = m(P - P_0)$.Substituting the values for $P = 60 \, cm$:$T - 0 = 2.5 	imes (60 - 50)$$T = 2.5 	imes 10$$T = 25^{\circ} C$.

$A$ constant volume gas thermometer shows pressure readings of $50 \, cm$ and $90 \, cm$ of mercury at $0^{\circ} C$ and $100^{\circ} C$ respectively. When the pressure reading is $60 \, cm$ of mercury,the temperature is ......... $^{\circ} C$.

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