Is gas volume of 444 mL at 273K and 79.0 kPa. What is the final kelvin temperature when the volume of the gas is changed to 1880 mL and the pressure changed to 38.7 kPa?

Md Ariful Islam

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We're asked to calculate the final absolute (Kelvin) temperature of a gas system when it is subdued to known pressure and volume changes.

To solve this problem, we can use the :

$(P_1V_1)/(T_1) = (P_2V_2)/(T_2)$

For this equation to work, the units have to be consistent; for example, we can't plug in two values for pressure if one is measured in $"kPa"$ and the other in $"atm"$; the units must be the same.

Since all the units are consistent, here, solving the problem is straightforward enough: we simply plug in the known variables and solve the equation for the final temperature, $T_2$:

$T_2 = (T_1P_2V_2)/(P_1V_1) = ((273"K")(38.7cancel("kPa"))(1880cancel("mL")))/((79.0cancel("kPa"))(444cancel("mL")))$

$= color(red)(566"K"$

rounded to $3$ , the number given in the problem.

Thus, the final Kelvin temperature after the changes in pressure and volume is $566"K"$

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