Question

question 6 (5 points)
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a sample of gas at a fixed pressure has a temperature of 300 k and a volume of 3 l. calculate the volume if the gas is heated to 700 k.
a) 5 l
b) 0.3 l
c) 3 l
d) 7 l

Explanation:

Step1: Identify the gas law

Since pressure is fixed, we use Charles's Law, which states that $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, where $V_1$ and $T_1$ are the initial volume and temperature, and $V_2$ and $T_2$ are the final volume and temperature.

Step2: List the given values

We have $V_1 = 3\space L$, $T_1 = 300\space K$, and $T_2 = 700\space K$. We need to find $V_2$.

Step3: Rearrange the formula to solve for $V_2$

From $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, we can rearrange it to $V_2=\frac{V_1\times T_2}{T_1}$.

Step4: Substitute the values into the formula

Substitute $V_1 = 3\space L$, $T_1 = 300\space K$, and $T_2 = 700\space K$ into the formula: $V_2=\frac{3\space L\times700\space K}{300\space K}$.

Step5: Calculate the result

First, calculate the numerator: $3\space L\times700\space K = 2100\space L\cdot K$. Then divide by the denominator: $\frac{2100\space L\cdot K}{300\space K}=7\space L$.

Answer:

D) 7 L