Question

Gas is confined in a metal tank in the figure. At 20.20°C, the gas exerts a pressure of 8.532 atm.
After heating the tank, the pressure of the gas increases to 10.406 atm. What is the temperature of
the heated gas?

Answer 1

Answer:

The temperature of  the heated gas is 357.6 K (or 84.6 C)

Explanation:

Gay Lussac's law indicates that, as long as the volume of the container containing the gas is constant, as the temperature increases, the gas molecules move faster. Then the number of collisions with the walls increases, that is, the pressure increases. That is, the pressure of the gas is directly proportional to its temperature.

In short, when there is a constant volume, as the temperature increases, the pressure of the gas increases. And when the temperature is decreased, the pressure of the gas decreases.

So, this law indicates that the quotient between pressure and temperature is constant:

$\frac{P}{T} =k$

You want to study two different states, an initial state 1 and a final state 2. Then it is true:

$\frac{P1}{T1} =\frac{P2}{T2}$

In this case:

• P1= 8.532 atm
• T1= 20.20 C= 293.2 K (being 0 C= 273 K)
• P2= 10.406 atm
• T2= ?

Replacing:

$\frac{8.532 atm}{293.2 K} =\frac{10.406 atm}{T2}$

Solving:

$T2*\frac{8.532 atm}{293.2 K} =10.406 atm$

$T2=10.406 atm*\frac{293.2 K}{8.532 atm}$

T2= 357.6 K

The temperature of  the heated gas is 357.6 K (or 84.6 C)

Answer 2

The new temperature of the heated gas when the pressure increase to 10.406 atm is 84.60 °C

Data obtained from the question

• Initial temperature (T₁) = 20.20°C = 20.20 + 273 = 293.20 K
• Initial pressure (P₁) = 8.532 atm
• Volume = constant
• New pressure (P₂) = 10.406 atm

• New temperature (T₂) =?

How to determine the new temperature

The new temperature of the gas can be obtained by using the combined gas equation as illustrated below:

P₁V₁ / T₁ = P₂V₂ / T₂

Since the volume is constant, we have:

P₁ / T₁ = P₂ / T₂

8.532 / 293.20 = 10.406 / T₂

Cross multiply

8.532 × T₂ = 293.20 × 10.406

Divide both side by 8.532

T₂ = (293.20 × 10.406) / 8.532

T₂ = 357.6 K

Subtract 273 from 357.6 K to express in degree celsius

T₂ = 357.6 – 273

T₂ = 84.60 °C

Learn more about gas laws:

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