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Question: The volume of a given mass of gas is 100 ml at \({\text{100 }}^\circ {\text{C}}\). If the pressure i...

The volume of a given mass of gas is 100 ml at 100 ∘C{\text{100 }}^\circ {\text{C}}. If the pressure is kept constant at what temperature (in100 ∘C{\text{100 }}^\circ {\text{C}}) will the sample have the volume of 200 ml.

Explanation

Solution

Use Charles’s law equation related to volume and temperature at constant pressure. Charles’s law states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.

Formula Used:
V1T1=V2T2\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}

Complete step-by-step answer: Calculate the temperature of the gas when the volume of gas increased from 100 ml to 200 ml at constant pressure as follows:
We have given initial volume, initial temperature and final volume of gas and we have to calculate the final temperature of the gas. As the pressure of a gas is constant use Charles’s law equation.
V1T1=V2T2\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}
Here,
V1{V_1} = initial volume of gas = 100 ml
V2{V_2} = final volume of gas = 200 ml
T1{T_1} = initial temperature =100∘C{\text{100}}^\circ {\text{C}}= (100 + 273)K = 373K{\text{(100 + 273)K = 373K}}
T2{T_2} = final temperature
Now, substitute 100 ml forV1{V_1}, 200 ml forV2{V_2}, 373K for T1{T_1} and solve the equation for the final temperatureT2{T_2}
100 ml373 K=200 mlT2\dfrac{{100{\text{ ml}}}}{{373{\text{ K}}}} = \dfrac{{200{\text{ ml}}}}{{{T_2}}}
T2= 746 K{T_2} = {\text{ 746 K}}
Now, convert this final volume of gas from Kelvin to degree Celcius.
T2= 746 K - 273K = 473 ∘C{T_2} = {\text{ 746 K - 273K = 473 }}^\circ {\text{C}}
So, an increase in temperature from 100 ∘C{\text{100 }}^\circ {\text{C}} to 473 ∘C{\text{473 }}^\circ {\text{C}} volume of gas increases from 100 ml to 200 ml.
Thus, the correct answer is 473 ∘C{\text{473 }}^\circ {\text{C}}

Note: According to Charles’s law at constant pressure, the volume of gas is directly proportional to the temperature of the gas. An increase in temperature increases the volume of gas. At constant pressure increase in temperature causes expansion of gas so the volume of gas increases. While the decrease in temperature decreases the volume of gas. In calculation always use the values of temperature in Kelvin.