Question

The volume of a gas varies inversely as the pressure and directly as the temperature (in degrees Kelvin). If acertain gas occupies a volume of 2.2 liters at a temperature of 340 K and a pressure of 16 newtons per squarecentimeter, find the volume when the temperature is 408 K and the pressure is 24 newtons per squarecentimeter.

Answer 1

The volume of the gas at 408 K and 24 N/cm² will be 1.76 liters, calculated using the combined gas law that integrates Boyle's law and Charles's law for the given changes in pressure and temperature.

Step-by-step explanation:

The volume of a gas is dependent on both its pressure and temperature, following Boyle's law and Charles's law, respectively. The relationship is such that volume varies inversely with pressure and directly with temperature (in kelvins) when the amount of gas is constant. To find the new volume when both the pressure and temperature change, we use the combined gas law, which integrates both Boyle's and Charles's laws:

V₁/T₁ * P₁ = V₂/T₂ * P₂

Given that at P₁ = 16 N/cm², T₁ = 340 K, and V₁= 2.2 liters, we can find V₂ when P₂ = 24 N/cm² and T₂ = 408 K using the formula:

V₂ = (V₁ * T₂/T₁) * (P₁/P₂)

Plugging in the values:

V₂ = (2.2 liters * 408 K / 340 K) * (16 N/cm² / 24 N/cm²)

V₂ = (2.2 liters * 1.2) * (2 / 3)

V₂ = 2.64 liters * (2 / 3)

V₂ = 1.76 liters

So, the volume of the gas when the temperature is 408 K and the pressure is 24 N/cm² would be 1.76 liters.

Answer 2

1.77 L

Step-by-step explanation:

The volume can be found using the following equation:

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

Where:

k: is a constant

T: is the temperature

P: is the pressure

With the values given:

V = 2.2 L

T = 340 K

P = 16 N/cm²

We can find the constant k:

`k = (PV)/(T) = (16 N/cm^(2)*2.2 L)/(340 K) = 0.104 N*L*K^(-1)*cm^(-2)`

Now ,we can find the volume when:

T = 408 K

P = 24 N/cm²

`V = (k*T)/(P) = (0.104 N*L*K^(-1)*cm^(-2)*408 K)/(24 Ncm^(-2)) = 1. 77 L`

Therefore, the volume is 1.77 L.

I hope it helps you!