The volume of a gas varies directly with the temperature and inversely with the pressure. When the temperature of a certain gas is 320Co, the pressure is 50 pounds per square inch and the volume is 30 cubic feet. Find the volume when the pressure is 60 pounds per square inch and the temperature decreases to 310Co.
V = kT/P
So, PV/T is constant. You want V such that
60V/(273+310) = 50*30/(273+320)
V = 24.578 ft^3
To solve this problem, we need to use the concept of direct and inverse variation.
Given:
Temperature (T1) = 320°C
Pressure (P1) = 50 psi
Volume (V1) = 30 cubic feet
We need to find:
Volume (V2) when Pressure (P2) = 60 psi and Temperature (T2) = 310°C.
According to the problem, the volume (V) varies directly with the temperature (T) and inversely with the pressure (P). This can be expressed as:
V ∝ T (direct variation)
V ∝ 1/P (inverse variation)
Combining these two proportionalities, we get:
V ∝ T / P
To apply this proportionality, we can set up the following equation:
V1 / T1 = V2 / T2
Substituting the given values:
30 / 320 = V2 / 310
Now we can solve for V2:
V2 = (30 * 310) / 320
= 9300 / 320
= 29.0625 cubic feet (approximately)
Therefore, when the pressure is 60 psi and the temperature decreases to 310°C, the volume of the gas will be approximately 29.0625 cubic feet.