assuming ideal gas behavior, which of the following variables are directly proportional to pressure?
□ amount (n)
□ temperature (t)
□ volume (v)

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Accepted Answer

# Explanation:
To determine which variables are directly proportional to pressure ($ P $) for an ideal gas, we use the ideal gas law: $ PV = nRT $, where $ P $ is pressure, $ V $ is volume, $ n $ is the amount of substance, $ R $ is the gas constant, and $ T $ is temperature (in Kelvin).

## Step 1: Analyze the relationship with amount ($ n $)
Rearranging the ideal gas law to solve for $ P $: $ P=\frac{nRT}{V} $. If we keep $ V $ and $ T $ constant, $ P $ is directly proportional to $ n $ (since $ P \propto n $ when $ V $ and $ T $ are constant). So, as $ n $ increases, $ P $ increases.

## Step 2: Analyze the relationship with temperature ($ T $)
From $ P=\frac{nRT}{V} $, if we keep $ n $ and $ V $ constant, $ P $ is directly proportional to $ T $ (since $ P \propto T $ when $ n $ and $ V $ are constant). So, as $ T $ increases, $ P $ increases.

## Step 3: Analyze the relationship with volume ($ V $)
From $ P=\frac{nRT}{V} $, $ P $ is inversely proportional to $ V $ (since $ P \propto \frac{1}{V} $ when $ n $ and $ T $ are constant). So, as $ V $ increases, $ P $ decreases, meaning they are not directly proportional.

# Answer:
- amount (n)
- temperature (T)

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QUESTION IMAGE

Question

Explanation:

Step 1: Analyze the relationship with amount (\( n \))

Step 2: Analyze the relationship with temperature (\( T \))

Step 3: Analyze the relationship with volume (\( V \))

Answer: