The volume V of a given mass of a gas varies directly as the temperature T and inversely as the pressure P.? If V=200 cm^3, T=40 degree and P=10 kg/cm^2, how do you find the volume when T=30 degree, P=5kg/cm^2?

Question

Isaiah Anthony · Accepted Answer

undefined To find the volume when T=30 degrees and P=5 kg/cm^2, we can use the direct variation and inverse variation formulas.

First, we need to set up the equation using the given values:
V = k * (T/P)

Next, we can solve for the constant of variation (k) by substituting the initial values:
200 = k * (40/10)

Simplifying the equation:
200 = k * 4
k = 200/4
k = 50

Now that we have the value of k, we can substitute it into the equation and solve for the volume when T=30 degrees and P=5 kg/cm^2:
V = 50 * (30/5)
V = 50 * 6
V = 300 cm^3

Therefore, the volume when T=30 degrees and P=5 kg/cm^2 is 300 cm^3.

Genesis Allen · Answer

The volume of gas is # 300 cm^3 # # V prop T , V prop 1/P #. Jointly #V prop T/P or V = k * T/P#, k is proporionality constant. # V=200 , T= 40 , P=10 # # V = k * T/P or k = (PV)/T= (10*200)/40=50 or k =50# # T=30 , P=5 , V= ?# The #P,V,T# equation is # V = k * T/P or V = 50 * 30/5 =300 cm^3 # The volume of gas is # 300 cm^3 # [Ans]