Question

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?

Answer 1

`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, " 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 = (2.45 / 1.75) * 292 = 408.8^@ K = 408.8 - 273 = 135.8^@ C`