Question

A given mass of gas occupied a volume of 500ml at 30°c. to what temperature must the gas be heated to make its final volume as 550ml. Assume that pressure of the gas remains constant ​

Answer 1

Given:

A given mass of gas occupied a volume of 500 ml at 30°C

Assume that pressure of the gas remains constant ​

To find:

To what temperature must the gas be heated to make its final volume as 550ml?

Solution:

The initial volume of the given gas = 500 ml

The initial temperature of the given gas = 30°C = 30 + 273 K = 303 K

The final volume of the given gas = 550 ml

Let's assume "T₂" represents the final volume of the gas.

We know that,

$\boxed{\bold{Charles'\: Law}} :\Rightarrow$ At constant pressure, the volume of a gas varies directly with its temperature(in Kelvin).

→ V ∝ kT ←

→ $\bold{\frac{V}{T}}$ = k

So, we get the equation representing the Charles' Law as:

$\boxed{\bold{\frac{V_1}{T_1} = \frac{V_2}{T_2} }}$

where

"V₁" → Initial Volume

"T₁" → Initial Temperature

"V₂" → Final Volume

"T₂" → Initial Temperature

Now, substituting V₁ = 500 ml, T₁ = 303 K & V₂ = 550 ml in the above equation of the law, we get

$\implies \frac{500}{303} = \frac{550}{T_2}$

$\implies T_2 = \frac{550 \times 303}{500}$

$\implies T_2 = \frac{166650}{500}$

$\implies \bold{T_2 = 333.3\:K}$

We will convert the temperature in Kelvin to Celcius

i.e., 333.3 K = 333.3 - 273 = 60.3 °C

Thus, assuming that pressure of the gas remains constant, the gas must be heated to a temperature of 60.3 °C to make its final volume as 550 ml.

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