# An ideal gas in a sealed container has an initial volume of 2.45 L. At a constant pressure, it is cooled to 19.00 °C where its volume is 1.75 L. What was initial temperature?

Aug 6, 2018

color(brown)("Initial Temperature " T_1 = 135.8^@ C

#### Explanation:

For a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature , assuming in a closed system.

${V}_{1} / {V}_{2} = {T}_{1} / {T}_{2} , \text{ where T is absolute temperature in KELVIN}$

"Given : V_1 = 2.45 L, V_2 = 1.75 L, T_2 = 19^@C = 273 + 19 = 292 ^@ K, T_1 = ?

${T}_{1} / {T}_{2} = {V}_{1} / {V}_{2}$

${T}_{1} = \left(\frac{2.45}{1.75}\right) \cdot 292 = {408.8}^{\circ} K = 408.8 - 273 = {135.8}^{\circ} C$