Question

A gas occupies a certain volume at 27 degree celcius.If it is heated at constant pressure, its volume is exactly doubled at a temperature of ----------------------

Answer 1

A gas occupies a certain volume at 27 degree Celsius. If it is heated at constant pressure, its volume is exactly doubled at a temperature of

Solution

Let's use the ideal gas law:

$$P * V = v * R * T.$$

Where $P$ is pressure of the gas, $V$ is volume of the gas, $T$ is temperature of the gas (in Kelvin), $v$ is amount of substance of gas, $R$ is the ideal gas constant.

Let assume $T_0 = 27{}^\circ C = (273 + 27)K = 300\,K$. As pressure $P$ is constant, then

$$2 * P * V = v * R * T_1 \rightarrow T_1 = \frac{2 * P * V}{v * R} = \frac{2 * (P * V)}{v * R} = \frac{2 * v * R * T_0}{v * R} = 2 * T_0.$$

So, the volume doubles when the temperature doubles. Here doubled temperature is

$$T_1 = 2 * 300\,K = 600\,K = (600 - 273){}^\circ C = 327{}^\circ C.$$

Answer: $327{}^\circ C$