Question

Gas Z in a cylinder at STP has a mass of 100 g. When the gas is compressed at 50 atm, the temperature of the gas increase to 850*celsius. Calculate the initial and final volume of the gas. (Mass of 1 mole of gas Z is 30 g, at STP: V =22.4 x 10 ^-3 m^-3 , T= 0*Celsius , P = 1 atm)

Answer 1

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Answer on Question #68149 Physics / Other

Gas Z in a cylinder at STP has a mass of $100\,\mathrm{g}$. When the gas is compressed at 50 atm, the temperature of the gas increases to $850{}^{\circ}\mathrm{celsius}$. Calculate the initial and final volume of the gas. (Mass of 1 mole of gas Z is $30\,\mathrm{g}$, at STP: $V = 22.4 \times 10^{-3}\,\mathrm{m}^3$, $T = 0{}^{\circ}\mathrm{Celsius}$, $P = 1\,\mathrm{atm}$).

Solution:

From the equation of state for perfect gas

$$PV = \frac{m}{\mu} RT$$

follows equation

$$V = \frac{m}{\mu} \frac{RT}{P}.$$

Using relations for SI units

$$1\,\mathrm{atm} = 10^{5}\,\mathrm{Pa}, \quad T\,(\mathrm{K}) = t\,({}^{\circ}\mathrm{C}) + 273$$

we obtain for initial volume

$$V_1 = \frac{m}{\mu} \frac{RT_1}{P_1} = \frac{100}{30} \times \frac{8.31 \times 273}{10^{5}} = 0.076\,\mathrm{m}^3,$$

and for final volume

$$V_2 = \frac{m}{\mu} \frac{RT_2}{P_2} = \frac{100}{30} \times \frac{8.31 \times 1123}{50 \times 10^{5}} = 0.006\,\mathrm{m}^3.$$

Answer: $V_1 = 0.076\,\mathrm{m}^3$, $V_2 = 0.006\,\mathrm{m}^3$.