Question

To what volume will a sample of gas expand if it is heated from 50.0°c and 2.33 l to 500.0°c?

Answer 1

The volume of the gas at $500^{\circ} \text{C}$ is $\fbox{\begin\ 5.576\,{\text{L}}\\\end{minispace}}$.

Further Explanation:

Consider the pressure of the gas to be constant.  

The change in the volume of the gas when the temperature of the gas is varied by keeping the pressure of the gas at a constant value is defined by the Charles' Law.

Concept:

According to the Charles law, the volume of the gas is directly proportional to the temperature of the gas at constant pressure.

The Charles' law can be stated as:

$\fbox{\begin\\V\propto T\\\end{minispace}}$

The above expression can we written as.

$\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$

Convert the temperature of the gas into kelvin.

$T=273+T^\circ\text{C}}}$

Here, T is the temperature in kelvin and $T^\circ\text{C}}}$ is the temperature in centigrade.  

The initial temperature of the gas is $50^\circ\text{C}$. The temperature of the gas in kelvin is.  

$\begin{aligned}{T_1}&=273+50\\&=323\,{\text{K}}\\\end{aligned}$

The final temperature of the gas is $500^\circ\text{C}$ . The temperature in kelvin is.  

$\begin{aligned}{T_2}&=273+500\\&=773\,{\text{K}}\\\end{aligned}$

Substitute the values of temperature and volume in the expression of the Charles' Law.  

$\begin{aligned}{V_2}&=\frac{{{T_2}}}{{{T_1}}}{V_1}\\&=\frac{{773\,{\text{K}}}}{{323\,{\text{K}}}}\left({2.33\,{\text{L}}}\right)\\&=5.576\,{\text{L}}\\\end{aligned}$

Thus, the volume of the gas at $500^\circ\text{C}}$ will be $\fbox{\begin\ 5.576\,{\text{L}}\\\end{minispace}}$.

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Answer Details:  

Grade: High school  

Subject: Physics  

Chapter: Gas law  

Keywords:  

Charles law, temperature, volume, initial, final, kelvin, centigrade, 50 C, 500 degree, 500 C, 50 degree, 2,33 L, gas expand, sample, heated.