Question

(9)Suppose that the Towngas supply pressure is 8.5 kPa (gauge pressure) andthe total volume is 2.4 m enters a building from outside where thetemperature is 10 °C and passes into a building where the temperature is 35°C, if the pressure was reduced to 2 kPa. What would be the new volume ofthe gas?

Answer 1

35.7 m³

Step-by-step explanation

By the ideal gases law,

`PV=nRT`

If we have the same gas in both situations, the product nR is constant, thus for this problem,

`\frac{P_{\text{out}}V_{\text{out}}}{T_{\text{out}}}=(P_(in)V_(in))/(T_(in))`

The given information is:

• Pout = 8500 Pa

,

• Pin = 2000 Pa

,

• Tout = 10 °C

,

• Tin = 35 °C

,

• Vout = 2.4 m³

,

• Vin =?

We have to solve the equation above for Vin,

`V_(in)=(T_(in))/(P_(in))\cdot\frac{P_{\text{out}}V_{\text{out}}}{T_{\text{out}}}`

Replace the values,

`V_(in)=(35C)/(2000Pa)\cdot(8500Pa\cdot2.4m^3)/(10C)=35.7m^3`

The new volume of the gas is 35.7 m³