Respuesta :
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
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
[tex]V =k \frac{T}{P}[/tex]
where;
k is constant of proportionality
make k subject of the formula
[tex]k = \frac{VP}{T} \\\\Thus, \frac{V_1P_1}{T_1} = \frac{V_2P_2}{T_2} \\\\V_2= \frac{V_1P_1T_2}{P_2T_1} \\\\V_2= \frac{42*8*185}{10*84} \\\\V_2 =74 \ cm^3[/tex]
Therefore, the final volume of the gas is 74 cm³
Answer:
V = 74 cm^3
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
