Examkin

Question

Difficulty: EasyDirect and Inverse Proportionality

A student measures the volume of a sample of gas at different temperatures while keeping the pressure constant. The data are shown in the table below:

Temperature (KK)Volume (LL)
1002.0
2004.0
3006.0
4008.0

Based on this table, which of the following mathematical relationships best describes the relationship between the temperature and the volume of the gas sample?

  1. A
    The volume is inversely proportional to the temperature.
  2. B
    The volume is independent of the temperature.
  3. The volume is directly proportional to the temperature.Answer
  4. D
    The volume decreases linearly as the temperature increases.

Answer

The volume is directly proportional to the temperature.
The correct answer shows that the volume is directly proportional to the temperature because the ratio of volume to temperature (V/TV/T) remains constant at 0.02 L/K0.02\text{ L/K} across all measured values. In a direct proportion, when one variable is multiplied by a factor, the other variable is multiplied by the same factor.

Step-by-Step Solution

1
Examine the direction of change for both variables in the table.
As the temperature increases from 100 K100\text{ K} to 400 K400\text{ K}, the volume also increases from 2.0 L2.0\text{ L} to 8.0 L8.0\text{ L}.
This rules out inverse relationships and independence, indicating a direct relationship.
2
Calculate the ratio of the volume (VV) to the temperature (TT) at each data point.
The ratio V/TV/T is constant: 2.0100=0.02 L/K\frac{2.0}{100} = 0.02\text{ L/K}, 4.0200=0.02 L/K\frac{4.0}{200} = 0.02\text{ L/K}, 6.0300=0.02 L/K\frac{6.0}{300} = 0.02\text{ L/K}, and 8.0400=0.02 L/K\frac{8.0}{400} = 0.02\text{ L/K}.
A constant ratio between two variables confirms that they are directly proportional.

Key Concept

Direct and Inverse Proportionality
Estimated Time:45s
Rate this question

Topics

Direct and Inverse Proportionality

More questions from this topic