Answer to Question #125081 in Physics for Raph

Question

A mass of a gas occupies 20 cm^3 at 5 degree celcius and 760 mm Hg pressure, what is its approximate volume at 30 degree celcius and 800 mm Hg pressure?

Answer 1

According to the general gas equation, the volume $V$, temperature $T$ and pressure $P$ of the ideal gas are connected in the following way:

$$\dfrac{PV}{T} = const$$

Thus, denoting with the index 1 parameters for the initial state and with the index 2 parameters for the final state, obtain:

$$\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}$$

Expressing the final volume from this equation, get:

$$V_2 = \dfrac{P_1V_1T_2}{P_2T_1}$$

Substituting the numerical value (and converting the temperature to kelvin), get:

$$V_2 = \dfrac{760\cdot 20\cdot (273+5)}{800\cdot (273+30)} \approx 17.4 cm^3$$

Answer. 17.4 cm^3.