A compressed gas has a pressure of 4.882 atm at a temperature of 8° C. The next day, the same container of gas has a pressure of 4.690 atm. What is the new temperature?

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A compressed gas has a pressure of 4.882 atm at a temperature of 8° C. The next day, the same container of gas has a pressure of 4.690 atm. What is the new temperature?

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Answer 1 · 2015-11-29T01:22:16

The new temperature will be $270. K$ $"270. K"$ , with three significant figures.

Explanation:

This is an example of Gay-Lussac's law, which states that when volume is kept constant, the pressure is directly proportional to the temperature in Kelvins.

The equation is $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ $P_1/T_1=P_2/T_2$

Given/Known
pressure 1: $P_{1} = 4.882 atm$ $P_1="4.882 atm"$
temperature 1: $T_{1} = 8^{o} C + 273.15 = 281 K$ $T_1=8^"o""C"+273.15="281 K"$
pressure 2: $P_{2} = 4.690 atm$ $P_2="4.690 atm"$

Unknown
temperature 2: $T_{2}$ $T_2$

Solution
Rearrange the equation to isolate $T_{2}$ $T_2$ and solve.

$T_{2} = \frac{T_{1} P_{2}}{P_{1}}$ $T_2=(T_1P_2)/P_1$

$T_{2} = \frac{(281 K \times 4.690 atm)}{4.882 atm} = 270. K$ $T_2=((281"K"xx4.690"atm"))/(4.882"atm")="270. K"$ (rounded to three significant figures)

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A compressed gas has a pressure of 4.882 atm at a temperature of 8° C. The next day, the same container of gas has a pressure of 4.690 atm. What is the new temperature?

1 Answer

Explanation:

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