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  • A sample of an ideal gas at a pressure of  and a volume of <img alt="0.1 \mathrm{~m

A sample of an ideal gas at a pressure of 2 \mathrm{~atm} and a volume of 0.1 \mathrm{~m}^3undergoes an isochoric process during which its pressure is increased to 4 \mathrm{~atm}. Calculate the final temperature of the gas.

Given that the gas constant \mathrm{R=8.314 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}} and the number of moles of the gas is 0.05 \mathrm{~mol}.
 

Option: 1

16.30 \mathrm{k}


Option: 2

17.20 \mathrm{k}


Option: 3

963.2 \mathrm{k}


Option: 4

20.4 \mathrm{k}


Answers (1)

best_answer

For an isochoric (constant volume) process, the relationship between the initial and final pressure\mathrm{ \left(P_i\right. and \left.P_f\right) } and temperature \mathrm{ \left(T_i\right. and \left.T_f\right) } of an ideal gas is given by:
\mathrm{\frac{P_f}{T_f}=\frac{P_i}{T_i} }
Given that \mathrm{P_i=2 \mathrm{~atm}, P_f=4 \mathrm{~atm}, T_i } (since the initial temperature is not given), and \mathrm{T_f } (what we want to find), we can solve for \mathrm{T_f }:
\mathrm{T_f=\frac{P_f}{P_i} \cdot T_i=\frac{4 \mathrm{~atm}}{2 \mathrm{~atm}} \cdot T_i=2 \cdot T_i }
Given that the number of moles of the gas is \mathrm{0.05 \mathrm{~mol} }, we can use the ideal gas law to relate pressure, volume, and temperature:
P V=n R T
Solving for \mathrm{T_i } :
\mathrm{T_i=\frac{P V}{n R} }
\mathrm{Substitute P=2 \mathrm{~atm} (convert\, \, to \, \, Pascals), V=0.1 \mathrm{~m}^3, n=0.05 \mathrm{~mol}, and R=8.314 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}: }
\mathrm{T_i=\frac{\left(2 \mathrm{~atm} \times 101325 \mathrm{~Pa} / \mathrm{atm} \times 0.1 \mathrm{~m}^3\right)}{(0.05 \mathrm{~mol} \times 8.314 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K})} \approx 481.6 \mathrm{~K} }
Therefore, the final temperature of the gas after the isochoric process is:
\mathrm{T_f=2 \cdot 481.6 \mathrm{~K}=963.2 \mathrm{~K} }
 

Posted by

Devendra Khairwa

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