Answer to Question #125082 in Physics for Raph

Question

A fixed mass of gas of volume 600 cm^3 at a temperature of 27 degree celcius is cooled at constant pressure to a temperature of 0 degree celcius, what is the change in volume?

Answer 1

According to the Charles's law, when a fixed mass of gas is is cooled at constant pressure, its temperature $T$ and volume $V$ obey the following equation:

$$\dfrac{V}{T} = k$$

Let's find the constant $k$. In the initial state:

$$k = \dfrac{V_1}{T_1} = \dfrac{600\cdot 10^{-6}m^3}{(273+27)K} = 2\cdot 10^{-6} m^3/K$$

After cooling, the new volume will be:

$$V_2 = kT_2 = 2\cdot 10^{-6} m^3/K\cdot 273K = 546\cdot10^{-6} m^3 = 546 cm^3$$

Answer. 546 cm^3.