Answer to Question #88019 in Optics for Amoo Emmanuel

Question

An ideal gas has a volume of 100cm3³ at 1.1*10^5Pa and 27°C. What is it volume at 2*10^5Pa and 60°C?

Answer 1

The equation of state of ideal gas is $p V = \nu R T$, where $p$ is pressure, $V$ is volume, $\nu$ is the number of moles, $T$ is the absolute temperature, and $R$ is the universal gas constant. From this equation, we obtain the ratio of volumes $V_1$ and $V_2$ at different corresponding values of pressure and absolute temperature $p_1, T_1$ and $p_2, T_2$:

$$\frac{V_2}{V_1} = \frac{p_1}{p_2} \frac{T_2}{T_1} \, .$$

According to the conditions, we have $V_1 = 100\, \text{cm}^3$, $p_1 = 1.1 \times 10^5\, \text{Pa}$, $T_1 = (27 + 273.15)\, \text{K} = 300.15\, \text{K}$, $p_2 = 2 \times 10^5\, \text{Pa}$, and $T_2 = (60 + 273.15)\, \text{K} = 333.15\, \text{K}$. Then $p_1 / p_2 = 0.55$ and $T_2 / T_1 \approx 1.11$, and we obtain

$$V_2 \approx 0.55 \times 1.11 V_1 \approx 0.61 \times 100\, \text{cm}^3 = 61 \, \text{cm}^3 \, .$$

Answer: 61 cm³.