For a certain gas in a closed container, the pressure has been raised by $0.4 %$ $0.4%$ , and the temperature was raised by $1 K$ $"1 K"$ . What temperature did the gas start at?

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For a certain gas in a closed container, the pressure has been raised by $0.4 %$ $0.4%$ , and the temperature was raised by $1 K$ $"1 K"$ . What temperature did the gas start at?

$a)$ $a)$ $250 K$ $"250 K"$
$b)$ $b)$ $200 K$ $"200 K"$
$c)$ $c)$ $298 K$ $"298 K"$
$d)$ $d)$ $300 K$ $"300 K"$

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Answer 1 · 2017-07-29T09:28:02

This is an impossible question. However, if we assume that the question should have written that the vessel is rigid, then I get an initial temperature of $250 K$ $"250 K"$ .

Well, as usual, when you see pressure, temperature, and "closed vessel" in the same sentence, we assume ideality...

$P V = n R T$ $PV = nRT$

$P$ $P$ is pressure in $atm$ $"atm"$ .

$V$ $V$ is volume in $L$ $"L"$ .

$n$ $n$ is mols of ideal gas.

$R = 0.082057 L \cdot atm/mol \cdot K$ $R = "0.082057 L"cdot"atm/mol"cdot"K"$ is the universal gas constant.

$T$ $T$ is temperature in $K$ $"K"$ (as it must be! Why?).

The closed vessel means very little to us; all it says is that the mols of gas are constant. It says nothing about the volume of the vessel being constant, as it could very well be a big fat balloon.

We apparently are given:

$P \to 1.004 P$ $P -> 1.004P$

$T \to T + 1$ $T -> T + 1$

$n \to n$ $n -> n$

$V \to ? ? ? \times V$ $V -> ??? xx V$

Substitute to get:

$1.004 P \cdot V = n R (T + 1) = n R T + n R$ $1.004P cdot V = nR(T+1) = nRT + nR$ ,

where the written variables are all for the initial state and we interpret the question to mean a closed AND rigid vessel. So, we assume that $? ? ? = 1$ $??? = 1$ .

Note that since $P V = n R T$ $PV = nRT$ , we can now write:

$1.004 n R T = n R (T + 1)$ $1.004nRT = nR(T + 1)$

Then, divide by $n R$ $nR$ to get:

$1.004 T = T + 1$ $1.004T = T + 1$

$\Rightarrow 0.004 T = 1$ $=> 0.004T = 1$

$\Rightarrow T = \frac{1}{0.004} = 250 K$ $=> color(blue)(T = 1/0.004 = "250 K")$

which is one of the given answer choices. It doesn't mean the question can't be revised, but that is probably what the question actually meant.

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... and beyond

For a certain gas in a closed container, the pressure has been raised by $0.4 %$ $0.4%$ , and the temperature was raised by $1 K$ $"1 K"$ . What temperature did the gas start at?

$a)$ $a)$ $250 K$ $"250 K"$
$b)$ $b)$ $200 K$ $"200 K"$
$c)$ $c)$ $298 K$ $"298 K"$
$d)$ $d)$ $300 K$ $"300 K"$

1 Answer

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Science

Math

Humanities

... and beyond

For a certain gas in a closed container, the pressure has been raised by 0.4%0.4%, and the temperature was raised by 1 K"1 K". What temperature did the gas start at?

a)a) 250 K"250 K" b)b) 200 K"200 K" c)c) 298 K"298 K" d)d) 300 K"300 K"

1 Answer

Related questions

Impact of this question

For a certain gas in a closed container, the pressure has been raised by $0.4 %$ $0.4%$ , and the temperature was raised by $1 K$ $"1 K"$ . What temperature did the gas start at?

$a)$ $a)$ $250 K$ $"250 K"$
$b)$ $b)$ $200 K$ $"200 K"$
$c)$ $c)$ $298 K$ $"298 K"$
$d)$ $d)$ $300 K$ $"300 K"$