Answer to Question #120012 in Molecular Physics | Thermodynamics for Samson

Question

Some hydrogen gas has a volume of 200cm3 at 150c. If the pressure remain constant at what temperature will its volume be 150cm3?

Answer 1

According to the Charles's law (see https://en.wikipedia.org/wiki/Charles%27s_law), when the pressure is kept constant, the temperature is proportional to volume. Therefore, we may write

$\dfrac{V_2}{V_1} = \dfrac{T_2}{T_1}$ .

Next, we substitute the given values and obtain

$\dfrac{150\,\mathrm{cm^3}}{200\,\mathrm{cm^3}}=\dfrac{T_2}{(150+273) \,\mathrm{K}}$ ; we should remember, that the temperature should be measured in Kelvins. Therefore, the temperature will be

$T_2 = (150+273)\cdot\dfrac{150\,\mathrm{cm^3}}{200\,\mathrm{cm^3}}\approx 317\,\mathrm{K} = (317-273)\,\mathrm{C} = 44^\circ\mathrm{C}.$