Question

The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P . Suppose that V= 42 cm^3 . when T = 84 kelvin and P = kg/cm^2 . Find the volume when T=185 kelvin and P = 10 kg/cm^2

Answer 1

V = 74 cm^3

Step-by-step explanation:

Solution:-

- The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Expressing the Volume (V) in terms of Temperature (T) and (P):

V ∝ T , V ∝ 1 / P

- Combine the two relations and equate the proportional relation with a proportionality constant:

V = k * (T / P)

Where, k: The proportionality constant:

- Using the given conditions and plug in the given relation of volume V:

Suppose that V= 42 cm^3 . when T = 84 kelvin , P = 8 kg/cm^2

k = V*P / T

k = 42*8 / 84

k = 4 kg cm / K

- Use the proportionality constant and evaluate Volume V for the following set of conditions:

T=185 kelvin and P = 10 kg/cm^2

V = 4*( 185 / 10 )

V = 74 cm^3

Answer 2

Complete question:

The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P . Suppose that V= 42 cm^3 . when T = 84 kelvin and P = 8 kg/cm^2 . Find the volume when T=185 kelvin and P = 10 kg/cm^2

Answer:

The final volume of the gas is 74 cm³

Step-by-step explanation:

Given;

initial volume of the gas, V₁ = 42 cm³

initial temperature of the gas, T₁ = 84 kelvin

initial pressure of the gas, P₁ = 8 kg/cm²

final volume of the gas, V₂ = ?

final temperature of the gas, T₂ = 185 kelvin

final pressure of the gas, P₂ = 10 kg/cm²

From the statement given in the question, we formulate mathematical relationship between Volume, V, Temperature, T, and Pressure, P.

V ∝ T ∝ ¹/p

`V =k (T)/(P)`

where;

k is constant of proportionality

make k subject of the formula

`k = (VP)/(T) \\\\Thus, (V_1P_1)/(T_1) = (V_2P_2)/(T_2) \\\\V_2= (V_1P_1T_2)/(P_2T_1) \\\\V_2= (42*8*185)/(10*84) \\\\V_2 =74 \ cm^3`

Therefore, the final volume of the gas is 74 cm³