If $\frac{9}{7} L$ $9/7 L$ of a gas at room temperature exerts a pressure of $12 k P a$ $12 kPa$ on its container, what pressure will the gas exert if the container's volume changes to $\frac{3}{4} L$ $3/4 L$ ?

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If $\frac{9}{7} L$ $9/7 L$ of a gas at room temperature exerts a pressure of $12 k P a$ $12 kPa$ on its container, what pressure will the gas exert if the container's volume changes to $\frac{3}{4} L$ $3/4 L$ ?

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Answer 1 · 2016-03-06T06:27:51

Gas will exert a pressure of $20.47 k P a$ $20.47kPa$

Explanation:

Pressure $P$ $P$ , volume $V$ $V$ and temperature $T$ $T$ (in Kelvin) have the relation $P \frac{V}{T} = k$ $PV/T=k$ where $k$ $k$ is a constant.

As no change in the temperature has been mentioned it is assumed to be constant at room temperature and then $P_{1} \times V_{1} = P_{2} \times V_{2}$ $P_1xxV_1=P_2xxV_2$

In the given case, $\frac{9}{7}$ $9/7$ $L$ $L$ of gas inside of a container exerts a pressure of $12 k P a$ $12kPa$ of pressure and is at a temperature of $30^{o} K$ $30^oK$ . When the volume of the gas changes to $\frac{3}{4}$ $3/4$ $L$ $L$ , the pressure becomes $P_{2}$ $P_2$ , we should have

$12 \times \frac{9}{7} = P_{2} \times \frac{3}{4}$ $12xx9/7=P_2xx3/4$ or $P_{2} = \frac{12 \times 9 \times 4}{3 \times 7} = \frac{144}{7} = 20.47$ $P_2=(12xx9xx4)/(3xx7)=144/7=20.47$

i.e. $P_{2} = 20.47 k P a$ $P_2=20.47kPa$

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If $\frac{9}{7} L$ $9/7 L$ of a gas at room temperature exerts a pressure of $12 k P a$ $12 kPa$ on its container, what pressure will the gas exert if the container's volume changes to $\frac{3}{4} L$ $3/4 L$ ?

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If $\frac{9}{7} L$ $9/7 L$ of a gas at room temperature exerts a pressure of $12 k P a$ $12 kPa$ on its container, what pressure will the gas exert if the container's volume changes to $\frac{3}{4} L$ $3/4 L$ ?